Question

I need some help with this compound interest problem in math????

Answer 1

$7,000((1 + .09/6)^72) = $20,448.11

$7,000(1 + .09)¹² = $19,688.65

After 12 years, the investment compounded periodically will be worth $759.46 more than the investment compounded annually.

Answer 2

$759.46

Explanation:

You want the difference in the value of $7000 accounts earning 9% interest for 12 years if one is compounded annually, and the other is compounded 6 times per year.

Compound interest

The formula for the value A of an investment P earning interest at rate r per year compounded n times per year for t years is ...

A = P(1 +r/n)^(nt)

You want the difference in the amounts when n = 6 and n = 1.

A = 7000(1 +.09/6)^(6·12) ≈ 20448.11

A = 7000(1 +.09/1)^(1·12) ≈ 19688.65

The difference is ...

20448.11 -19688.65 = 759.46

The investment compounded periodically will be worth $759.46 more after 12 years.

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