QuestionSeptember 19, 2025

Find the balance of a savings plan after 36 months assuming an APR of 10% (compounded monthly) and monthly deposits of 105. 4,387.09 4,297.26 4,413.90 4,256.88 None of the above.

Find the balance of a savings plan after 36 months assuming an APR of 10% (compounded monthly) and monthly deposits of 105. 4,387.09 4,297.26 4,413.90 4,256.88 None of the above.
Find the balance of a savings plan after 36 months assuming an APR of 10%  (compounded monthly) and monthly deposits of 105.
 4,387.09
 4,297.26
 4,413.90
 4,256.88
None of the above.

Solution
4.1(273 votes)

Answer

None of the above. Explanation 1. Identify the formula for future value of an ordinary annuity Use FV = P \frac{(1 + r)^n - 1}{r}, where P is monthly deposit, r is monthly interest rate, n is number of deposits. 2. Substitute values P = 105, APR = 10\%, so r = \frac{0.10}{12} = 0.008333, n = 36. 3. Calculate (1 + r)^n (1 + 0.008333)^{36} \approx 1.34885 4. Compute numerator and denominator Numerator: 1.34885 - 1 = 0.34885; Denominator: 0.008333 5. Calculate future value FV = 105 \times \frac{0.34885}{0.008333} \approx 105 \times 41.862 \approx 4,395.51

Explanation

1. Identify the formula for future value of an ordinary annuity<br /> Use $FV = P \frac{(1 + r)^n - 1}{r}$, where $P$ is monthly deposit, $r$ is monthly interest rate, $n$ is number of deposits.<br />2. Substitute values<br /> $P = 105$, $APR = 10\%$, so $r = \frac{0.10}{12} = 0.008333$, $n = 36$.<br />3. Calculate $(1 + r)^n$<br /> $(1 + 0.008333)^{36} \approx 1.34885$<br />4. Compute numerator and denominator<br /> Numerator: $1.34885 - 1 = 0.34885$; Denominator: $0.008333$<br />5. Calculate future value<br /> $FV = 105 \times \frac{0.34885}{0.008333} \approx 105 \times 41.862 \approx 4,395.51$
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