Answer and Explanation:
Given:
Amount that parents wish to have is future value = $37,000
Time period (nper) = 17 years
Rate = 8.4% or 0.084
Use spreadsheet function =pmt(rate,nper,FV) to compute yearly payment to savings account.
New parents need to deposit $1,057.14 at the end of every year.
Interest earned during 17 years = FV - (annual payment × 17)
= 37,000 - (1057.14×17)
= $19,028.62
Interest earned during 17 years is $19,028.62
Value of fund after 10 years is future value of fund which can be computed using spreadsheet function =FV(rate,nper,-pmt)
nper is 10 years
Value of fund after 10 years is $15,608.31
In order to compute interest earned during 10 year, first future value of fund in 9th year need to be computed using spreadsheet function =FV(rate,nper,-pmt)
nper is 9 years
Value of fund after 10 years is $13,423.59
Interest earned = Value of savings in 10th year - Value of savings in 9th year - amount deposited in the 10th year
= 15,608.31 - 13,423.59 - 1,057.14
= $1,127.58
Interest earned in 10th year is $1,127.58
1. The amount that the parents should place at the end of each year into the savings account is $1,057.14.
2. The interest they would earn over the life of the savings account is $19,028.66.
3. The value of the fund after 10 years is $15,608.27.
4. The interest earned during the 10th year alone is $1,127.58.
Data and Calculations:
N (# of periods) = 17 years
I/Y (Interest per year) = 8.4%
PV (Present Value) = 0
FV (Future Value) = $37,000
Results:
Annual Payment = $1,057.14
Sum of all periodic payments = $17,971.34
Total Interest = $19,028.66
Schedule
Period PV PMT Interest FV
1 $0.00 $-1,057.14 $0.00 $1,057.14
2 $-1,057.14 $-1,057.14 $-88.80 $2,203.08
3 $-2,203.08 $-1,057.14 $-185.06 $3,445.27
4 $-3,445.27 $-1,057.14 $-289.40 $4,791.81
5 $-4,791.81 $-1,057.14 $-402.51 $6,251.46
6 $-6,251.46 $-1,057.14 $-525.12 $7,833.72
7 $-7,833.72 $-1,057.14 $-658.03 $9,548.89
8 $-9,548.89 $-1,057.14 $-802.11 $11,408.14
9 $-11,408.14 $-1,057.14 $-958.28 $13,423.56
10 $-13,423.56 $-1,057.14 $-1,127.58 $15,608.27
Thus, the savings account will be worth $37,000 after 17 years with a total contribution by the parents of $17,971.34 and total interest earned of $19,028.66.
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