Question 12 of 15 , step 1 of 1
Andrew deposits a fixed monthly amount into an annuity account for his child’s college fund. He wishes to accumulate a future value of in 14 years. Assuming an
APR of compounded monthly, how much of the will Andrew ultimately deposit in the account, and how much is interest earned? Round your answers to
the nearest cent, if necessary.
Formulas

Ask by Gross Newton. in the United States

Jan 24,2025

Question

Question 12 of 15 , step 1 of 1
Andrew deposits a fixed monthly amount into an annuity account for his child’s college fund. He wishes to accumulate a future value of in 14 years. Assuming an
APR of compounded monthly, how much of the will Andrew ultimately deposit in the account, and how much is interest earned? Round your answers to
the nearest cent, if necessary.
Formulas

Ask by Gross Newton. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To determine how much Andrew will ultimately deposit in the account and the interest earned, we'll follow these steps:

1. **Calculate the Monthly Deposit (P):**

We can use the future value formula for an ordinary annuity:

$$
   \text{FV} = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
   $$

Where:
   - $$\text{FV} = \$65,000$$ (Future Value)
   - $$r = \frac{3.6\%}{12} = 0.003$$ (Monthly interest rate)
   - $$n = 14 \times 12 = 168$$ (Total number of monthly deposits)

Rearranging the formula to solve for $$P$$:

$$
   P = \frac{\text{FV}}{\left( \frac{(1 + r)^n - 1}{r} \right)}
   $$

Plugging in the values:

$$
   P = \frac{65,000}{\left( \frac{(1 + 0.003)^{168} - 1}{0.003} \right)}
   $$

Calculating $$(1 + 0.003)^{168}$$:

$$
   (1.003)^{168} \approx 1.65407
   $$

Then:

$$
   \frac{1.65407 - 1}{0.003} \approx 218.0239
   $$

So:

$$
   P \approx \frac{65,000}{218.0239} \approx 298.16
   $$

**Monthly Deposit (P):** $$\$298.16$$

2. **Calculate the Total Deposits (VA):**

$$
   \text{Total Deposits} = P \times n = 298.16 \times 168 \approx 50,091.72
   $$

**Total Deposited:** $$\$50,091.72$$

3. **Calculate the Interest Earned:**

$$
   \text{Interest Earned} = \text{Future Value} - \text{Total Deposits} = 65,000 - 50,091.72 \approx 14,908.28
   $$

**Interest Earned:** $$\$14,908.28$$

**Final Answer:**

- **Total Deposited:** \$50,091.72
- **Interest Earned:** \$14,908.28
Andrew will deposit a total of \$50,091.72 over 14 years, and the interest earned will be \$14,908.28.

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