To calculate the future value of an investment compounded semiannually, you can use the formula: ( A = P \left(1 + \frac{r}{n}\right)^{nt} ), where ( A ) is the amount of money accumulated after n years, including interest, ( P ) is the principal amount (6700), ( r ) is the annual interest rate (0.046), ( n ) is the number of times that interest is compounded per year (2), and ( t ) is the number of years the money is invested (15).
Plugging in the values:
( A = 6700 \left(1 + \frac{0.046}{2}\right)^{2 \times 15} )
( A = 6700 \left(1 + 0.023\right)^{30} )
( A = 6700 \left(1.023\right)^{30} \approx 6700 \times 2.0304 \approx 13,619.18 ).
Thus, the investment will be worth approximately $13,619.18 in 15 years.
1200
I haven't gotten the answer to that test question either....the choices seem wrong
The rate is 15.56%. The amount invested is irrelevant in this calculation.
If every six months the capital earn 10% interest which is compounded, at the end of 5 years, the interest will be 31875. If the annual interest rate is 10%, it makes no difference how often it is compounded. The six monthly interest rate is adjusted - to 4.88% rather than 5% - so that the total interest for a year is 10%.
The annual equivalent rate is 15.5625%. The amount invested is irrelevant to calculation of the equivalent rate.
$5,249.54
1200
The future value of $600 invested for 5 years at an 8% interest rate compounded semiannually can be calculated using the formula FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, P = $600, r = 8% = 0.08, n = 2 (since interest is compounded semiannually), and t = 5. Plugging these values into the formula, we get FV = 600(1 + 0.08/2)^(2*5) = $925.12. Therefore, the future value of the investment after 5 years would be $925.12.
Semiannually over two years is equivalent to 4 periods. If the interest is 12% every 6 months, then the amount of interest is It is 8000*[(1.12)4 -1] =4588.15
I haven't gotten the answer to that test question either....the choices seem wrong
The rate is 15.56%. The amount invested is irrelevant in this calculation.
If every six months the capital earn 10% interest which is compounded, at the end of 5 years, the interest will be 31875. If the annual interest rate is 10%, it makes no difference how often it is compounded. The six monthly interest rate is adjusted - to 4.88% rather than 5% - so that the total interest for a year is 10%.
If the interest is compounded annually, then the first interest payment isn't added until the end of the first year. Until then, the investment is worth exactly $15,000.00 .
SupposeCapital invested = YAnnual Interest Rate = R%Period of investment = TThen if the interest is calculated (and compounded) n times a yeartotal value =Y*[1 + r/(100*n)]^(n*T)So interest accrued = Total value - YSupposeCapital invested = YAnnual Interest Rate = R%Period of investment = TThen if the interest is calculated (and compounded) n times a yeartotal value =Y*[1 + r/(100*n)]^(n*T)So interest accrued = Total value - YSupposeCapital invested = YAnnual Interest Rate = R%Period of investment = TThen if the interest is calculated (and compounded) n times a yeartotal value =Y*[1 + r/(100*n)]^(n*T)So interest accrued = Total value - YSupposeCapital invested = YAnnual Interest Rate = R%Period of investment = TThen if the interest is calculated (and compounded) n times a yeartotal value =Y*[1 + r/(100*n)]^(n*T)So interest accrued = Total value - Y
The annual equivalent rate is 15.5625%. The amount invested is irrelevant to calculation of the equivalent rate.
10001/999900
To calculate the future value of an investment compounded semiannually, you can use the formula: [ A = P \left(1 + \frac{r}{n}\right)^{nt} ] where: ( A ) is the amount of money accumulated after n years, including interest. ( P ) is the principal amount (5000). ( r ) is the annual interest rate (0.06). ( n ) is the number of times that interest is compounded per year (2 for semiannual). ( t ) is the number of years the money is invested (10). Plugging in the values: [ A = 5000 \left(1 + \frac{0.06}{2}\right)^{2 \times 10} = 5000 \left(1 + 0.03\right)^{20} = 5000 \left(1.03\right)^{20} \approx 5000 \times 1.8061 \approx 9030.50 ] Thus, $5000 would grow to approximately $9030.50 in ten years at 6 percent compounded semiannually.