Question

Jamar has invested $300 in an annuity each month, earning 5.5% interest for 30 years.

Beth has invested $600 in an annuity each month, earning 5.5% interest for 15 years.

Which of the following must be true?

Select the correct answer below:

Answer 1

(d) Jamar's ending account balance is higher than Beth's ending balance.

Explanation:

You want to know the best description of the relationship between final balances of two ordinary annuities:

• 300 per month for 30 years at 5.5%
• 600 per month for 15 years at 5.5%

Future value

The attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.

Jamar's balance: $274,083.57

Beth's balance: $167,247.33

The best description is ...

Jamar's ending account balance is higher than Beth's ending balance.

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Additional comment

Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.