Answer to Question #225430 in Financial Math for Aman

Question

3. A loan of $36,550.00 at 5.00% compounded semi-annually is to be repaid with payments at the end of every 6 months. The loan was settled in 5 years.

 

a. Calculate the size of the periodic payment. Round to the nearest cent.

 b. Calculate the total interest paid. Round to the nearest cent.

Answer 1

a)

Interest rate =5%

Semi-annual interest rates $=\frac{5}{2}=2.5\%$

Payment period =5 years =10 semi-annual

Present value FACTOR $=\frac{1-(1+r)^{-n}}{r}$  

Present value FACTOR $=\frac{1-(1.025)^{-10}}{0.025}=8.752063931$

Loan amount =Present value FACTOR x semi-annual payment 

$36550=8.7520663931 ×$ semi-annual payment 

Semi-annual payment $=\$4176.157$

Total payment = Semi-annual payment x number of payments 

Total payment $=10 × 4176.157=41761.57$

Total payment $=\$41761.57$

b)

$Interest =Total \space payment- loan \space amount \\ Interest =41761.57 - 36550\\ Interest =\$5211.57\\$