Question

Use the compound interest formulas, A = P (1 + rn ) nt and A = Pe rt, to solve. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 5.5% if the money is a. compounded semiannually. b. compounded monthly. c. compounded continuously.

Answer 1

Answer:

(a) $13116.51

(b) $1315.03

(c) $12762.81

Explanation:

We have given principal amount P = $10000

Rate of interest r = 5.5 %

Time = 5 years

(a) When compounded semiannually

Rate of interest $=\frac{5.5}{2}=2.75$ %

Time period n= 5×2=10 period  

So amount after 5 year

$A=P(1+\frac{r}{100})^n=10000\times (1+\frac{2.75}{100})^{10}= 13116.51$

(b)  When compounded monthly

Rate of interest $=\frac{5.5}{12}=0.4583$ %

Time period n= 5×12=60 period  

So amount after 5 year

$A=P(1+\frac{r}{100})^n=10000\times (1+\frac{0.4583}{100})^{60}= 13157.03$

(c) When compounded continuously

Rate of interest = 5.5 %

Time period n= 5 year

So amount after 5 year

$A=P(1+\frac{r}{100})^n=10000\times (1+\frac{5}{100})^{5}= 12762.81$