Question

Spence wants to have $176,000 in 7 years. He plans to make regular savings contributions of $13,100 per year for 7 years, with the first of these regular savings contributions made in 1 year. He also expects to make a special savings contribution of X in 3 years. He expects to earn 17.18 percent per year. What is X, the amount of the special savings contribution that Spence will make in 3 years?

Answer 1

$11,098.94

Step-by-step explanation:

first we must calculate the future value of the 7 year annuity:

FV of an annuity = p x {[(1 + r)ⁿ - 1] / r}

• p = $13,100
• r = 17.18%
• n = 7

FV of an annuity = $13,100 x {(1.1718⁷ - 1) / 0.1718} = $13,100 x 11.8377 = $155,073.56

since he wants to have $176,000, he needs $20,926.44 more in 7 years (= $176,000 - $155,073.56)

X = FV / (1 + r)ⁿ

• future value =
• n = 4 years
• r = 17.18%

X = $20,926.44 / 1.1718⁴ = $11,098.94