In how many years will a certain sum of money be three times at 20% per annum simple interest ✅ Đã Test
Mẹo về In how many years will a certain sum of money be three times 20% per annum simple interest 2022
Cao Nguyễn Bảo Phúc đang tìm kiếm từ khóa In how many years will a certain sum of money be three times 20% per annum simple interest được Cập Nhật vào lúc : 2022-10-14 11:30:53 . Với phương châm chia sẻ Kinh Nghiệm về trong nội dung bài viết một cách Chi Tiết Mới Nhất. Nếu sau khi Read Post vẫn ko hiểu thì hoàn toàn có thể lại Comment ở cuối bài để Ad lý giải và hướng dẫn lại nha.A. 8 years
Nội dung chính- Solution(By Examveda Team) Simple Interest Formula Compound Interest Formula Compounding Periods Other Compounding Interest Concepts Time Value of Money The Rule of 72 Compound Annual Growth Rate (CAGR) Real-Life Applications Additional Interest Considerations The Bottom Line In what time will a sum becomes three times itself 20% per annum simple interest?In what time 10% per annum simple interest a sum becomes 3 times of itself?How many years will a principal 8% per annum simple interest becomes three times of the principal?How long will it take for an amount to become 5 times of itself 20% per annum simple interest?
B. 10 years
C. 12 years
D. 14 years
Solution(By Examveda Team)
$$eqalign & textLet principal = P cr & therefore textamount = 3P cr & textInterest = 3P - textP cr & ,,,,,,,,,,,,,,,,,,,,,text = 2P cr & textAccording to the question, cr & text2P = fractextP times textR times
text20100 cr & Rightarrow textR = 10% cr $$
Let after t years it will become double
$$eqalign & textHence, cr & textInterest = 2P - textP = P cr & Rightarrow textP = fractextP times 10 times textt100 cr & Rightarrow textt = 10 years cr $$
Interest is defined as the cost of borrowing money, as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit, as in the case of a certificate of deposit. Interest can be calculated in two ways: simple interest or compound interest.
- Simple interest is calculated on the principal, or original, amount of a loan.Compound interest is
calculated on the principal amount and the accumulated interest of previous periods, and thus can be regarded as “interest on interest.”
There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound basis rather than on a simple basis. On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation.
While simple interest and compound interest are basic financial concepts, becoming thoroughly familiar with them may help you make more informed decisions when taking out a loan or investing.
Simple Interest Formula
The formula for calculating simple interest is:
Simple Interest = P × i × n where: P = Principal i = Interest rate n = Term of the loan beginaligned&textSimple Interest = P times i times n \&textbfwhere:\&P = textPrincipal \&i = textInterest rate \&n = textTerm of the loan \endaligned Simple Interest=P×i×nwhere:P=Principali=Interest raten=Term of the loan
Thus, if simple interest is charged 5% on a $10,000 loan that is taken out for three years, then the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.
Interest on this loan is payable $500 annually, or $1,500 over the three-year loan term.
Compound Interest Formula
The formula for calculating compound interest in a year is:
Compound Interest = ( P ( 1 + i ) n ) − P Compound Interest = P ( ( 1 + i ) n − 1 ) where: P = Principal i = Interest rate in percentage terms n = Number of compounding periods for a year beginaligned &textCompound Interest = big ( P(1 + i) ^ n big ) - P \ &textCompound Interest = P big ( (1 + i) ^ n - 1 big ) \ &textbfwhere:\ & P= textPrincipal\ &i = textInterest rate in percentage terms \ &n = textNumber of compounding periods for a year \ endaligned Compound Interest=(P(1+i)n)−PCompound Interest=P((1+i)n−1)where:P=Principali=Interest rate in percentage termsn=Number of compounding periods for a year
Compound Interest = total amount of principal and interest in future (or future value) less the principal amount present, called present value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return.
Continuing with the simple interest example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be:
Interest = $ 10 , 000 ( ( 1 + 0.05 ) 3 − 1 ) = $ 10 , 000 ( 1.157625 − 1 ) = $ 1 , 576.25 beginaligned textInterest &= $10,000 big( (1 + 0.05) ^ 3 - 1 big ) \ &= $10,000 big ( 1.157625 - 1 big ) \ &= $1,576.25 \ endaligned Interest=$10,000((1+0.05)3−1)=$10,000(1.157625−1)=$1,576.25
While the total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into consideration the accumulated interest of previous periods. Interest payable the end of each year is shown in the table below.
Year Opening Balance (P) Interest 5% (I) Closing Balance (P+I) 1 $10,000.00 $500.00 $10,500.00 2 $10,500.00 $525.00 $11,025.00 3 $11,025.00 $551.25 $11,576.25 Total Interest $1,576.25 WATCH: What is Compound Interest?
Compounding Periods
When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 of a loan over a certain period, the amount of interest accrued 10% annually will be lower than the interest accrued 5% semiannually, which will, in turn, be lower than the interest accrued 2.5% quarterly.
In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year.
That is, within the parentheses, “i” or interest rate has to be divided by “n,” the number of compounding periods per year. Outside of the parentheses, “n” has to be multiplied by “t,” the total length of the investment.
Therefore, for a 10-year loan 10%, where interest is compounded semiannually (number of compounding periods = 2), i = 5% (i.e., 10% ÷ 2) and n = 20 (i.e., 10 x 2).
To calculate the total value with compound interest, you would use this equation:
Total Value with Compound Interest = ( P ( 1 + i n ) n t ) − P Compound Interest = P ( ( 1 + i n ) n t − 1 ) where: P = Principal i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan beginaligned &textTotal Value with Compound Interest = Big( P big ( frac 1 + in big ) ^ nt Big ) - P \ &textCompound Interest = P Big ( big ( frac 1 + in big ) ^ nt - 1 Big ) \ &textbfwhere: \ &P = textPrincipal \ &i = textInterest rate in percentage terms \ &n = textNumber of compounding periods per year \ &t = textTotal number of years for the investment or loan \ endaligned Total Value with Compound Interest=(P(n1+i)nt)−PCompound Interest=P((n1+i)nt−1)where:P=Principali=Interest rate in percentage termsn=Number of compounding periods per yeart=Total number of years for the investment or loan
The following table demonstrates the difference that the number of compounding periods can make over time for a $10,000 loan taken for a 10-year period.
Compounding Frequency No. of Compounding Periods Values for i/n and nt Total Interest Annually 1 i/n = 10%, nt = 10 $15,937.42 Semiannually 2 i/n = 5%, nt = 20 $16,532.98 Quarterly 4 i/n = 2.5%, nt = 40 $16,850.64 Monthly 12 i/n = 0.833%, nt = 120 $17,059.68
Other Compounding Interest Concepts
Time Value of Money
Since money is not “không lấy phí” but has a cost in terms of interest payable, it follows that a dollar today is worth more than a dollar in the future. This concept is known as the time value of money and forms the basis for relatively advanced techniques like discounted cash flow (DFC) analysis. The opposite of compounding is known as discounting. The discount factor can be thought of as the reciprocal of the interest rate and is the factor by which a future value must be multiplied to get the present value.
The formulas for obtaining the future value (FV) and present value (PV) are as follows:
FV = P V × [ 1 + i n ] ( n × t ) PV = F V ÷ [ 1 + i n ] ( n × t ) where: i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan beginaligned&textFV=PVtimesleft[frac1+inright]^(ntimes t)\&textPV=FVdivleft[frac1+inright]^(ntimes t)\&textbfwhere:\&i=textInterest rate in percentage terms\&n=textNumber of compounding periods per year\&t=textTotal number of years for the investment or loanendaligned FV=PV×[n1+i](n×t)PV=FV÷[n1+i](n×t)where:i=Interest rate in percentage termsn=Number of compounding periods per yeart=Total number of years for the investment or loan
The Rule of 72
The Rule of 72 calculates the approximate time over which an investment will double a given rate of return or interest “i” and is given by (72 ÷ i). It can only be used for annual compounding but can be very helpful in planning how much money you might expect to have in retirement.
For example, an investment that has a 6% annual rate of return will double in 12 years (72 ÷ 6%).
An investment with an 8% annual rate of return will double in nine years (72 ÷ 8%).
Compound Annual Growth Rate (CAGR)
The compound annual growth rate (CAGR) is used for most financial applications that require the calculation of a single growth rate over a period.
For example, if your investment portfolio has grown from $10,000 to $16,000 over five years, then what is the CAGR? Essentially, this means that PV = $10,000, FV = $16,000, and nt = 5, so the variable “i” has to be calculated. Using a financial calculator or Excel spreadsheet, it can be shown that i = 9.86%.
Please note that according to cash flow convention, your initial investment (PV) of $10,000 is shown with a negative sign since it represents an outflow of funds. PV and FV must necessarily have opposite signs to solve “i” in the above equation.
Real-Life Applications
CAGR is extensively used to calculate returns over periods for stocks, mutual funds, and investment portfolios. CAGR is also used to ascertain whether a mutual fund manager or portfolio manager has exceeded the market’s rate of return over a period. For example, if a market index has provided total returns of 10% over five years, but a fund manager has only generated annual returns of 9% over the same period, then the manager has underperformed the market.
CAGR can also be used to calculate the expected growth rate of investment portfolios over long periods, which is useful for such purposes as saving for retirement. Consider the following examples:
A risk-averse investor is happy with a modest 3% annual rate of return on their portfolio. Their present $100,000 portfolio would, therefore, grow to $180,611 after 20 years. In contrast, a risk-tolerant investor who expects an annual rate of return of 6% on their portfolio would see $100,000 grow to $320,714 after 20 years.CAGR can be used to estimate how much needs to be stowed away to save for a specific objective. A couple who would like to save $50,000 over 10 years toward a down payment on a condo would need to save $4,165 per year if they assume an annual return (CAGR) of 4% on their savings. If they’re prepared to take on additional risk and expect a CAGR of 5%, then they would need to save $3,975 annually.CAGR can also be used to demonstrate the virtues of investing earlier rather than later in life. If the objective is to save $1 million by retirement age 65, based on a CAGR of 6%, a 25-year-old would need to save $6,462 per year to attain this goal. A 40-year-old, on the other hand, would need to save $18,227, or almost three times that amount, to attain the same goal.Additional Interest Considerations
Make sure you know the exact annual percentage rate (APR) on your loan since the method of calculation and number of compounding periods can have an impact on your monthly payments. While banks and financial institutions have standardized methods to calculate interest payable on mortgages and other loans, the calculations may differ slightly from one country to the next.
Compounding can work in your favor when it comes to your investments, but it can also work for you when making loan repayments. For example, making half your mortgage payment twice a month, rather than making the full payment once a month, will end up cutting down your amortization period and saving you a substantial amount of interest.
Compounding can work against you if you carry loans with very high rates of interest, like credit card or department store debt. For example, a credit card balance of $25,000 carried an interest rate of 20%—compounded monthly—would result in a total interest charge of $5,485 over one year or $457 per month.
The Bottom Line
Get the magic of compounding working for you by investing regularly and increasing the frequency of your loan repayments. Familiarizing yourself with the basic concepts of simple interest and compound interest will help you make better financial decisions, saving you thousands of dollars and boosting your net worth over time.
In what time will a sum becomes three times itself 20% per annum simple interest?
=>N=10 years. Was this answer helpful?In what time 10% per annum simple interest a sum becomes 3 times of itself?
∴ Time is 8 years.How many years will a principal 8% per annum simple interest becomes three times of the principal?
T=20 years It takes 20 years.How long will it take for an amount to become 5 times of itself 20% per annum simple interest?
`rArr 4x = (x xx n xx 20)/(100)`
`rArr 4 = (n)/(5) rArr n= 20`
`therefore` In 20 years, the sum becomes 5 times itself.
Hence, the correct option is (a). Tải thêm tài liệu liên quan đến nội dung bài viết In how many years will a certain sum of money be three times 20% per annum simple interest
