Question

An engineer deposits $2,000 per month for four years at a rate of 24% per year, compounded semiannually.
How much will he be able to withdraw 10 years after his last deposit ?

Answer 1

Solution:-

In order to answer this question, it is essential that we first draw a timeline to fully understand the problem. I have attached the workings and timeline of this problem below.

First, we convert the deposits that are monthly, into semiannual deposits. We do this by simply multiplying the monthly deposit of $2000 by 6 to get $12000.

Then, we convert the 24% yearly interest rate into semiannual by dividing it by 2. This gives us r=12%

We also convert the number of periods 'n' in a semiannual form by multiplying the number of years 4*2 as each year is going to have 2 periods (semi-annual).

Then, we find the Future value of this annuity at year 4.

Using the formula shown in the workings, we get the Future value of this annuity.

Next, we need to find the future value of our deposits at year 14 (4+10).

We do this by using the previously found Future value as the PV@year 4 and getting the future value FV@year14

In doing so, we use the same semi-annual interest rate 12% and number of periods 'n' now becomes 10*2=20 periods.

Further calculations shown in the picture result in the value of $1,423,757.26 as the amount that can be withdrawn after 10 years of last deposit.