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

a) $11,940.52

b) $11,956.18

c) $11,966.81

d) $11,910.16

Step-by-step explanation:

Given:

Investment amount = $10,000

Time = 3 years

Interest rate = 6%

Now,

Amount =
`P*(1+(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*(1+(0.06)/(2))^(2*3)`

Amount = $10000 × 1.03⁶

or

Amount = $11,940.52

b) compounded​ quarterly

n = 4

`Amount = \$10,000*(1+(0.06)/(4))^(4*3)`

Amount = $10000 × 1.015¹²

or

Amount = $11,956.18

c) compounded​ monthly

n = 12

`Amount = \$10,000*(1+(0.06)/(12))^(12*3)`

Amount = $10000 × 1.00536³⁶

or

Amount = $11,966.81

d) compounded​ continuously

n = 12

`Amount = \$10,000*(1+(0.06)/(1))^(1*3)`

Amount = $10000 × 1.06³

or

Amount = $11,910.16