Calculating time value of money (Future values/Present values)

Question

Mrs PQ is saving for her daughter’s education in five (5) years’ time. Her estimation is that tuition and living costs will be $300 000. She decides to deposit $3 000 per month (at the beginning of each month) into an interest-bearing account, where she can earn 12% per annum compounded monthly.

1. Will Mrs PQ be able to meet her target at the end of the five-year period? Also determine whether there will be a surplus or shortfall after five years. (4)
2. Determine the exact amount that Mrs PQ needs to deposit at the beginning of each month to achieve her goal. (3)

Answer 1

Hi Jack,

You can either use Excel, a financial calculator or perform the calculation by hand. Assuming you are using technology, you can use the following inputs:

N = 5 * 12 = 60 (months, 5 years, 12 months each)

i = 12% / 12 = 1% per month

PMT = -3,000 (cash outflow into the account)

PV = $0, the saver has nothing now

FV = future value is what we are solving for.

In Excel, this produces the result of: which is obviously not enough to make the goal.

For part 2, you can find the goal to save by solving for payments:

N = 60 (same amount of time)

i = 12% / 12 = 1% (same rate)

Future Value (FV) = $300,000

PV = 0 nothing being saved today

PMT = what we are solving for (payments)

In Excel, this produces the resut of $ which means the saver needs to put this amount in the account each month.

I hope this was helpful for you. Contact me for a special session discount if you need more help!

Patrick