Find the Value of an Annuity
-Kurt deposits $150 each month into an account paying annual interest of 6% compounded monthly. How much will his account have in it at the end of 9 years?
A) $21,411
B) $1724
C) $21,257
D) $21,540

Question

Quizplus · Accepted Answer

The correct answer is A.The future value of an annuity is given by the formula:FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)where:P is the monthly depositr is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsIn this case, we have:P = $150r = 6% = 0.06n = 12 (since the interest is compounded monthly)t = 9Plugging these values into the formula, we get:FV = $150 * ((1 + 0.06/12)^(12*9) - 1) / (0.06/12)= $150 * ((1.005)^108 - 1) / 0.005= $150 * (2.1411 - 1) / 0.005= $150 * 214.11 / 0.005= $21,411Therefore, Kurt's account will have $21,411 in it at the end of 9 years.