Solve the problem.
-Which of the following investments is larger after 10 years?
A) An initial amount of $\$ 12,000$ is deposited with $\$ 6000$ deposited annually, with interest earned at $5.75 \%$ compounded annually.
B) An initial amount of $\$ 10,000$ is deposited with $\$ 500$ deposited monthly, with interest earned at $5.75 \%$ compounded monthly.

Question

Quizplus · Accepted Answer

The future value of an annuity is given by the formula:$$FV = P * \frac{(1 + r)^n - 1}{r}$$where:* FV is the future value* P is the principal (initial amount)* r is the annual interest rate* n is the number of yearsFor investment A, we have:* P = $12,000* r = 5.75% = 0.0575* n = 10Plugging these values into the formula, we get:$$FV = 12000 * \frac{(1 + 0.0575)^{10} - 1}{0.0575} = $24,726.27$$For investment B, we have:* P = $10,000* r = 5.75% = 0.0575* n = 10 * 12 = 120 (since interest is compounded monthly)Plugging these values into the formula, we get:$$FV = 10000 * \frac{(1 + 0.0575/12)^{120} - 1}{0.0575/12} = $24,657.67$$Therefore, investment A is larger after 10 years.

Solve the Problem $12,000\$ 12,000$12,000 Is Deposited With $6000\$ 6000$6000 Deposited Annually, with Interest Earned At

Solve the Problem $\$ 12,000$ Is Deposited With $\$ 6000$ Deposited Annually, with Interest Earned At