SOLUTION: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year,

Question 1190278: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 7.5%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old.
How much money will they have to have saved by the time they are 60 in order to reach their retirement goal?
If they do live the full 30 years, and spend their full quarterly budget, how much money in total will they have lived on/spent in their retirement?
How much will have been earned in interest?
If they saved the same total amount of their own money, but no interest earned over the years whatsoever, how much would be available to live on each quarter?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can use the following calculator to solve this.

https://arachnoid.com/finance/index.html

here are the results of using that calculator to find the present value of 12000 at the beginning of each quarter for 30 * 12 = 120 quarters.

inputs are everything except present value.
output is present value = 581,832.99.

you will have spent a total of 120 * 12000 = 1,440,000 over the 30 year period.

your interest earned would have been 1,440,000 minus 581,832.99 = 858,167.01.

the interest rate per quarter was 7.5/4 = 1.875%.

the number of quarters was 30 * 4 = 120.

if you were not earning any interest on the money that you saved, the you would have had 4848.61 available at the beginning of each quarter.

that was calculated by changing the interest rate per quarter to 0 and solving for the payment, as shown below.

inputs were everything except pmt.
output was pmt.

let me know if you have any questions.

theo

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