1. **State the problem:** A friend has an IRA with an APR of 5.75% compounded monthly. She deposits 100 per month starting at age 25 and retires at age 65. We want to find the amount in the IRA at retirement and compare it to the total deposits made. 2. **Identify variables:** - APR (annual interest rate) = 5.75% = 0.0575 - Monthly interest rate $i = \frac{0.0575}{12} = 0.0047917$ - Number of years $t = 65 - 25 = 40$ - Number of months $n = 40 \times 12 = 480$ - Monthly deposit $P = 100$ 3. **Use the future value of an ordinary annuity formula:** $$ A = P \times \frac{(1+i)^n - 1}{i} $$ 4. **Calculate:** $$ A = 100 \times \frac{(1+0.0047917)^{480} - 1}{0.0047917} $$ Calculate $(1+0.0047917)^{480}$: $$ (1.0047917)^{480} \approx 7.0391 $$ Then: $$ A = 100 \times \frac{7.0391 - 1}{0.0047917} = 100 \times \frac{6.0391}{0.0047917} \approx 100 \times 1260.07 = 126007 $$ 5. **Total deposits:** $$ \text{Total deposits} = P \times n = 100 \times 480 = 48000 $$ 6. **Interpretation:** The IRA will contain approximately 126007 at retirement. The total deposits made over 40 years are 48000. **Final answers:** - IRA amount at retirement: $126007.00$ - Total deposits: $48000$