Question

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 will be made. If the effective annual interest rate is 4% this period of time, what are the annual deposits (A) in years 5 through 15? Please round your answer to the nearest integer. $3,200 $2,800 $2,400 $2,000 5th Birthday 6 Years 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 1 1 1 1 A = ?

Answer 1

Assume that annual deposit = X

Amount of withdrawls mentioned in diagram:

18th Year= $2,000

19th Year= $2,400

20th year= $2,800

21st year= $3,200

We first need to find Present worth of total deposit at the end of the year of 18th year:

= $2,000 + [$2,400 x (PVF, 4%, 1 year)] + [$2,800 x (PVF, 4%, 2 year)] + [$3,200 x (PVF, 4%, 3 year)]

= $2,000 + $2,307.69 + $2,588.75 + $2,844.78

= $9,741.22

$9,741.22 this is the size of deposit of 18th year, which is due to annual deposits made between year (5-15).

Again find the Present worth of size of deposit $9,741.22 at the end of the year 18th year:

PW of deposit at EOY 15th year = $9,741.22 x PVF @ 4% for 3 years

= $8,659.91

Now these annual deposits made between year 5 to year 15:

X (PVF @ 4% for 10 years) = $8,659.91

Time duration is between 15 - 5 =10 years

X (8.1109) = $8,659.91

X = $1,067.69

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