# a problem related to geometric progression

on the birth of a child, an aunt promises "I will deposit $100.00 in an account today and on every birthday until your 25th". Simple interest of 7.5% per annum is paid on this account. How much will be in the account after the deposit on the 25th birthday? solution:$S_n = a\frac{ r^n - 1}{r-1}S_n = 100 \frac{1.075^{25} - 1}{1.075 - 1} =6797.79$but answer given is$5037.50

• Are you sure this is geometric progression? – peterwhy Nov 11 '14 at 14:48
• I find it to be 7407.6! Are you sure about 5037.5? – Jimmy R. Nov 11 '14 at 14:49
• perhaps answer is wrong, pls guide how to solve this question...THANKS – sekling Nov 11 '14 at 14:53

## 1 Answer

Hint: Since the interest is not compounded, the first deposit of $\$100$earns a total interest of $$\100\times7.5\% \times 25 = \187.5$$ And the second deposit of$\$100$ earns a total interest of $$\100\times7.5\%\times24 = \180$$ $$\vdots$$ The last deposit when the child is 25 years old earns a total interest of $\$0$. • Maybe, because the problem states that it's "Simple interest"? :3 And pay attention that the deposit money in the bank will grow$100 more each year (I haven't included the interest). – user49685 Nov 11 '14 at 15:07
• great,total principle deposit = $2600 and total interest =$2437.50 so total amount = \$5037.50 – sekling Nov 11 '14 at 15:10
• I am using excel to derive the answer, however pls guide whether any suitable formula can be used to calculate this out?? – sekling Nov 11 '14 at 15:11
• Big hint of the day: It's an arithmetic progression. :3 – user49685 Nov 11 '14 at 15:14
• yes, SIMPLE INTEREST is the interest payable only on the principal; interest that is not compounded. – sekling Nov 11 '14 at 15:15