Question

Find the accumulated value of an investment of $ 10 comma 000 for 3 years at an interest rate of 6 % if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded monthly d. compounded continuously.

Answer 1

Answer:

a) $11,940.52

b) $11,956.18

c) $11,966.81

d) $11,910.16

Explanation:

Given:

Investment amount = $10,000

Time = 3 years

Interest rate = 6%

Now,

Amount = $P\times(1+\frac{r}{n})^{nt}$

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Thus,

a) compounded​ semiannually

n = 2

$Amount = \ 10,000\times(1+\frac{0.06}{2})^{2\times3}$

Amount = $10000 × 1.03⁶

or

Amount = $11,940.52

b)  compounded​ quarterly

n = 4

$Amount = \ 10,000\times(1+\frac{0.06}{4})^{4\times3}$

Amount = $10000 × 1.015¹²

or

Amount = $11,956.18

c)  compounded​ monthly

n = 12

$Amount = \ 10,000\times(1+\frac{0.06}{12})^{12\times3}$

Amount = $10000 × 1.00536³⁶

or

Amount = $11,966.81

d) compounded​ continuously

n = 12

$Amount = \ 10,000\times(1+\frac{0.06}{1})^{1\times3}$

Amount = $10000 × 1.06³

or

Amount = $11,910.16