So here is the problem:Luke is borrowing $\$10{,}000$ from the bank. The bank offers him a choice between two $10$-year payment plans:

Plan 1 Luke's debt accumulates $10\%$ annual interest which compounds quarterly. Luke pays off half his balance after $5$ years, and the rest at the end of the $10$ years.

Plan 2 Luke's debt accumulates $10\%$ annual interest which compounds annually. Luke pays off his full balance at the end of the $10$ years.

What is the (positive) difference between Luke's total payments under Plan 1 and his total payments under Plan 2? Round to the nearest dollar.

Now, the second plan's payment amount is $10,000 * (1 +\frac{1}{10})^{10}$ which is around $25937$.

In the first plan, he will pay off $\frac{1}{2} *10000 (1+\frac{1}{10})^{20}$ after five years. The remaining amount will continue to be compounded, which he pays off after another five years, which is $\frac{1}{2} * 10000(1+\frac{1}{10})^{40}$ which is around 259933. The difference between the plans is a lot. Where did I go wrong?

  • $\begingroup$ Please read the tag description before choosing the tag. $\endgroup$ – N. F. Taussig Apr 27 '18 at 14:54
  • 3
    $\begingroup$ If the annual rate for plan 1 is 10%, then the quarterly factor should be $(1 + \frac{0.10}{4})$, shouldn't it? And the number of quarters in $5$ years is $20$. $\endgroup$ – MPW Apr 27 '18 at 14:54
  • $\begingroup$ Please don't use MathJax for normal text. MathJax is for objects in mathematical discourse. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Apr 27 '18 at 14:56
  • $\begingroup$ Oh.... I see what you mean. So my mistake was thinking the annual rate is the same as the quarterly rate/ $\endgroup$ – TheLeogend Apr 27 '18 at 14:56
  • $\begingroup$ Is MathJax like Latex? Where you put dollar signs around the numbers? $\endgroup$ – TheLeogend Apr 27 '18 at 14:59

On calculating the first plan, $\frac 12*10000(1+\frac{1}{10})^{20}$ should be replaced by $10000(1+\frac{2.5}{100})^{20}$ because in the FIRST FIVE years the interest is being compounded quarterly on the complete amount. The interest rate is 10% per year and not 10% per quarter.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.