New parents wish to save for their newborn's education and wish to have $37,000 at the end of 17 years. How much should the pare
nts place at the end of each year into a savings account that earns an annual rate of 8.4% compounded annually? (Round your answers to two decimal places.)$ How much interest would they earn over the life of the account?$ Determine the value of the fund after 10 years.$ How much interest was earned during the 10th year?$
1 answer:
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
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