SOLUTION: Frank has deposited $1000 at the end of each year into a retirement savings plan for the last 10 years.His deposits earned interest at j=8% for the first 3 years,at j=10.25% for th

Question 1194021: Frank has deposited $1000 at the end of each year into a retirement savings plan for the last 10 years.His deposits earned interest at j=8% for the first 3 years,at j=10.25% for the next 4 years,and at j=9% for the last 3 years.
a) what is accumulated value of his retirement plan?
b) what is the total interest earned for the 10 years?
c) find an equivalent interest rate (same for 10 years ),which conducts to the same results of a) and b).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the calculator i used for this is the ti-ba-ii busness analyst by texas instruments.

for the first part, the inputs were:
present value = 0
payment at the end of each year = 1000
number of years = 3
interest rate per year = 8%
output was future value = 3246.4

for the second part, the inputs were:
present value = -3246.4
payment at the end of each year = -1000
number of years = 4
interest rate per year 10.25%
output was future value = 9454.513243

for the third part, the inputs were:
present value = -9454.513243
payment at the end of each year = -1000
number of years = 3
interest rate per year = 9%
output was future value = 15521.96883

the total investment was 1000 * 3 + 1000 * 4 + 1000 * 3 = 10,000
the total interest earned was 15,521.96883 minus 10,000 = 5,521.96883.

for the last part, the inputs were:
present value = 0
payment at the end of each year = -1000
number of years = 10
future value = 15521.96883
output was interest rate = 9.448451033%

here's what it looks like in a year by year display using excel.

here's what the inputs and outputs look like using arachnoid financial calculator at https://arachnoid.com/finance/index.html

any differences in results are due to intermediate rounding by the online calculator.

let me know if you have any questions.
theo
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