Question

Greg deposited $4000 into an account with 4.6% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 7 years?

Answer 1

The amount in account after 7 years is $ 5499.445

Solution:

The formula for total amount in compound interest is given as:

`A = p(1+(r)/(n))^(nt)`

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here given that,

A = ?

P = 4000

t = 7 years

`r = 4.6 \% = (4.6)/(100) = 0.046`

n = 2 ( since compounded semi annually)

Substituting the values in formula, we get

`A = 4000(1+(0.046)/(2))^(2 * 7)\\\\Simplify\ the\ above\ expression\\\\A = 4000(1+0.023)^(14)\\\\A = 4000(1.023)^(14)\\\\A = 4000 * 1.37486\\\\A = 5499.445`

Thus amount in account after 7 years is $ 5499.445