Answer to Question #280806 in Financial Math for vangie

Question

bellamy borrowed 65,000 at 7% interest compounded quarterly and agreed to repay the loan in quarterly payments of 5,000 each . the first payment is due in two years. Find the number of payments

Answer 1

Given,

Quarterly Payments= 5,000

Principle Amount = 65,000

Rate = 7% p.a

principle=payment

$[\frac{1-(1+\frac{r}{n})^{-nt}}{\frac{r}{n}}]\\ 65 000=5000 [\frac{1-(1+\frac{0.07}{4})^{-4t}}{\frac{0.07}{4}}]\\ 65 000=5000 [\frac{1-(1+0.0175)^{-4t}}{\frac{0.07}{4}}]\\ \frac{65 000}{5 000}=[\frac{1-(1-0.0175)^{-4t}}{0.175}]\\ 12\times 0.0175=[1-(1.0175)^{-4t}]\\0.2275=1-0.0175^{-4t}\\0.7725=1.0175^{-4t}$

Now taking log on both sides,

$log (0.7725)=log(1.0175)^{-4t}\\ log (0.7725)=-4t log(1.0175)\\t=\frac{log (0.7725)}{-4t log(1.0175)}\\t=3.7196$

Therefore, total number of payments if made quarterly will be:

number of payments

$=3.7196\times 4\\=14.8784\\ around \space 15 \space payments$