Question

Deshaun deposited $4000 into an account with 5.1% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years?

Answer 1

`A = 4652.37 \text{dollars}`

is the amount after 3 years!

Explanation:

Data:

`P` = 4000 initial amount

`n` = rate at which the interest is applied per period = 2 times per year.

`t` = periods = 3 years

`n* t` = number of times the interest is applied = 2*3= 6 times.

`r` = interest rate = 5.1% = 0.051

Now we can use our compound interest formula:

`A = P\left(1+(r)/(n)\right)^(n* t)`

`A = 4000\left(1+(0.051)/(2)\right)^(6)`

`A = 4652.37 \text{dollars}`

is the amount after 3 years!

Answer 2

A = $4652.37

Explanation:

Given:

Initial amount (P) = $4000

Interest rate (r) = 5.1 %

n = 2 (Compounding per year)

t = 3 years

Using Compound interest formula:

`A =P(1+ r/n )^(nt)\\\\A = 4000( 1 + (0.051/2))^(2*3)\\A = $4652.37`