Question

Score: 0 of 1 pt | 4 of 7 (5 complete) HW Score: 66.67%, & Problem 4-81 (algorithmic) Question H Suppose that the parents of a young child decide to make annual deposits into a savings account, with the first deposit being made on the child's fifth birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the withdrawals as shown on the diagram below will be made. If the effective annual interest rate is 8% during this period of time, what are the annual deposits in years 5 through 15? Use a uniform gradient amount (G) in your solution. Click the icon to view the diagram for cash flows. Click the icon to view the interest and annuity table for discrete compounding when i More Info The annual deposits in years 5 through 15 are $ 461. (Round to the nearest cent.) 3,350 2,900 2,450 2,000 0 0 3 5th Years i= 8%/yr 9 10 11 12 13 14 Birthday6 7 8 15 16 17 18 19 20 21 A = ? Print Done

Answer 1

Formula: The Future Value of an annuity due (FV)

FV= {C× {[(1+r)^n]-1}/r} x (1+r)

FV = Future value (The cummulative amount available in t=16, look at image) = 8071.11
C= Periodic cash out flow. ?
r =effective interest rate for the period. 0.08
n = number of periods. 11

8071.11 = {C× {[(1+0.08)^11]-1}/0.08} x (1+0.08)

C= 448.97

The uniform amount to be deposited from 5th Birthday to 15th birthday is $448.97

+ + 5 6 18 19 20 21 Value of Benefits at time = 15 (+-15) 2000 + 2450 + 2900 + 3350 (1.08)3 (108) 4 - 8) (1.08) (1.0806 = 7,473.25 Value - at t = 16 7473. 25 *(1.08) - 8071.11