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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

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  • $\begingroup$ Are you sure this is geometric progression? $\endgroup$ – peterwhy Nov 11 '14 at 14:48
  • $\begingroup$ I find it to be 7407.6! Are you sure about 5037.5? $\endgroup$ – Jimmy R. Nov 11 '14 at 14:49
  • $\begingroup$ perhaps answer is wrong, pls guide how to solve this question...THANKS $\endgroup$ – sekling Nov 11 '14 at 14:53
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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 $\$0$.

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  • $\begingroup$ 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). $\endgroup$ – user49685 Nov 11 '14 at 15:07
  • $\begingroup$ great,total principle deposit = $2600 and total interest = $2437.50 so total amount = $5037.50 $\endgroup$ – sekling Nov 11 '14 at 15:10
  • $\begingroup$ I am using excel to derive the answer, however pls guide whether any suitable formula can be used to calculate this out?? $\endgroup$ – sekling Nov 11 '14 at 15:11
  • $\begingroup$ Big hint of the day: It's an arithmetic progression. :3 $\endgroup$ – user49685 Nov 11 '14 at 15:14
  • $\begingroup$ yes, SIMPLE INTEREST is the interest payable only on the principal; interest that is not compounded. $\endgroup$ – sekling Nov 11 '14 at 15:15

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