Question

At the beginning of year 1, Carlos invests $600 at an annual compound interest rate of 4%. He makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 5? What is, the balance?

Answer 1

I believe your answer would be B.

Answer 2

B.
`A(n)=600(1+0.04)^(n-1); \$701.92`

Explanation:

Since, the amount formula in compound interest,

`A=P(1+r)^t`

Where, P is the principal amount ( or initial amount ),

r is the annual interest,

t is time ( in years )

Here,

The invested amount is $ 600 at the beginning of year 1,

⇒ P = $ 600

r = 4 % = 0.04

Thus, the amount after n-1 years or the beginning of n years would be,

`A=600(1+0.04)^(n-1)`

Which is the required explicit formula,

If n = 5,

Then, the amount at the beginning of 5th year,

`A=600(1+0.04)^(5-1)=600(1.04)^4=\$ 701.915136\approx \$701.92`

Hence, Option 'B' is correct.