Exponential percentage increase equation

Question

I’d like an equation for the following, and how to work it out on the calculator please!

55000 x 10%, + 4000 being added after every period, x 12 periods.

i can use an exponential growth calculator to work out 55000 x 10% for 12 periods, but adding 4000 to the amount after each period and then increasing it all by 10% 12 times is what throws me.

Thanks

Answer 1

This looks like a Future Value Of Annuity problem (initial investment of 55000 dollars, interest rate at 10%) with 4000 dollars being added at the end of each period for 12 periods.

The correct solution (which agrees with an online annuity calculator that I consulted) is given by:

55000 times (1 + 0.10) + 4000 gives 64500 at end of Period 1.

64500 times (1 + 0.10) + 4000 gives 74590 at end of Period 2.

74590 times (1 + 0.10) + 4000 gives 86445 at end of Period 3.

86445 times (1 + 0.10) + 4000 gives 99089.50 at end of Period 4.

99089.50 times (1 + 0.10) + 4000 gives 112998.45 at end of Period 5.

112998.45 times (1 + 0.10) + 4000 gives 128298.295 at end of Period 6.

128298.295 times (1 + 0.10) + 4000 gives 145128.1245 at end of Period 7.

145128.1245 times (1 + 0.10) + 4000 gives 163640.937 at end of Period 8.

163640.937 times (1 + 0.10) + 4000 gives 184005.0306 at end of Period 9.

184005.0306 times (1 + 0.10) + 4000 gives 206405.5337 at end of Period 10.

206405.5337 times (1 + 0.10) + 4000 gives 231046.0871 at end of Period 11.

231046.0871 times (1 + 0.10) + 4000 gives 258150.6958 at end of Period 12.

Code for a Casio Programmable Calculator (Model fx-7000G) is:

0→N

55000→S

4000→P

Lbl 7

1.1S + P→S∴ (Stop and show contents of S.)

1 + N→N

N = 12⇒N∴ (If N equals 12, then stop and show contents of N.)

Go to 7 (Return to Lbl 7 and repeat the loop.)