use the compound interest formulas ( a = pleft(1+\frac{r}{n}\right)^{nt} ) and ( a = pe^{rt} ) to solve the…

use the compound interest formulas ( a = pleft(1+\frac{r}{n}\right)^{nt} ) and ( a = pe^{rt} ) to solve the problem given. round answers to the nearest cent.\nfind the accumulated value of an investment of $10,000 for 5 years at an interest rate of 4.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.\na. what is the accumulated value if the money is compounded semiannually?\n$ 12492.03\n(round your answer to the nearest cent. do not include the $ symbol in your answer.)\nb.what is the accumulated value if the money is compounded quarterly?\n$ square\n(round your answer to the nearest cent. do not include the $ symbol in your answer.)

use the compound interest formulas ( a = pleft(1+\frac{r}{n}\right)^{nt} ) and ( a = pe^{rt} ) to solve the problem given. round answers to the nearest cent.\nfind the accumulated value of an investment of $10,000 for 5 years at an interest rate of 4.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.\na. what is the accumulated value if the money is compounded semiannually?\n$ 12492.03\n(round your answer to the nearest cent. do not include the $ symbol in your answer.)\nb.what is the accumulated value if the money is compounded quarterly?\n$ square\n(round your answer to the nearest cent. do not include the $ symbol in your answer.)

Answer

Explanation:

Step1: Identify values

Given ( P = 10000 ), ( r = 4.5% = 0.045 ), ( t = 5 ), compounded quarterly so ( n = 4 ).

Step2: Apply compound interest formula

The formula is ( A = P\left(1+\frac{r}{n}\right)^{nt} ). Substitute values: ( A = 10000\left(1+\frac{0.045}{4}\right)^{4\times5} ). First, calculate ( \frac{0.045}{4}=0.01125 ), ( 4\times5 = 20 ). Then, ( 1 + 0.01125 = 1.01125 ). Next, ( 1.01125^{20} \approx 1.249413 ). Finally, ( A = 10000\times1.249413 \approx 12494.13 ).

Answer:

12494.13