29
QuizMultiple Choice

N/A — Exam

Question 29 • Financial Math

You invest $⁢100 monthly in an annuity that pays 5% interest, compounded monthly, for 30 years. What will be the annuity's future value? Formula for future value of an annuity: F⁢V=P×((1+r/n)^n⁢t−1)/(r/n) where: • F⁢V = future value of the annuity • P = payment amount per period • r = annual interest rate (decimal) • n = number of compounding periods per year • t = total number of years

Answer
A
37 dollars comma 800 point 0 0
B
83 dollars comma 225 point 8 6
C
3 dollars comma 188 point 5 0
D
6 dollars comma 643 point 8 8

Explanation

Use P = 100, r = 0.05, n = 12, and t = 30 in the annuity formula. There are 12 × 30 = 360 monthly payments, and the monthly interest rate is 0.05 ÷ 12. Substituting gives 100 × ((1 + 0.05/12)^360 − 1) ÷ (0.05/12) ≈ $83,225.86. The future value is choice B, $83,225.86.

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