Question

cain deposited $6033 into savings account 25 years ago the account has an interest rate of 4.2 and the balance is currently $7208.63 how often does the interest compound

Answer 1

interest is compounded monthly

Explanation:

there is a slight mistake in the question, the future value after 25 years is $17,208.63, not $7,208.63

the future value = present value x (1 + i/a)ⁿᵃ

future value = $17,208.63

present value = $6,033

i/a = 4.2%/a

n x a = 25a

(1 + 0.042/a)²⁵ᵃ = $17,208.63 / $6,033 = 2.852416708

²⁵√(1 + 0.042/a)²⁵ᵃ = ²⁵√2.852416708

(1 + 0.042/a)ᵃ = 1.042818

4.2818% would be the effective interest on the loan, so we can try different options for a. Since the effective interest is higher, I will try first with monthly compounding:

a = 12 (compounded monthly)

(1 + 0.042/12)¹² = (1 + 0.0035)¹² = 1.042818 ✓