Question

1. A year ago, you deposited $30,000 into a retirement savings account at a fixed rate of 5.5 percent. Today, you could earn a fixed rate of 6.5 percent on a similar type account. However, your rate is fixed and cannot be adjusted. How much less could you have deposited last year if you could have earned a fixed rate of 6.5 percent and still have the same amount as you currently will when you retire 38 years from today?

Answer 1

Ans:- In this question, first we need to find the future value at the rate of 5.5% if $30,000 deposited today, and then we will discount that future value at the rate of 6.5% to get the Present Value. After that, we will subtract it from $30,000 to know how much we less could have deposited to get the same amount at 6.5%.

Future Value = Present Value*(1+r)^n, where r is the annual rate and n is the number of periods.

Present Value = $30,000, r=5.5%, and n =39 (since it was deposited 1 year ago and retirement year remaining from today is 38 years so total will be 39 years).

FV = $30,000*(1+5.5%)^39 = $242,084.61.

Now the Present Value of this Future Value, if it was deposited at 6.5%, will be

= $242,084.61 / (1+ 6.5%)^39 = $20,765.03.

Note:- PV = Future Value / (1+r)^n

Now, the difference between the amount is $30,000 - $20,765.03 = $9,234.97.

Therefore, if $9,234.97 less amount was deposited 1 year ago at the rate of 6.5% it will give the same amount at retirement what $30,000 will give at 5.5%.

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