Question #225430

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.


1
Expert's answer
2021-08-12T15:02:35-0400

a)

Interest rate =5%

Semi-annual interest rates =52=2.5%=\frac{5}{2}=2.5\%

Payment period =5 years =10 semi-annual

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

Present value FACTOR =1(1.025)100.025=8.752063931=\frac{1-(1.025)^{-10}}{0.025}=8.752063931

Loan amount =Present value FACTOR x semi-annual payment 

36550=8.7520663931×36550=8.7520663931 × semi-annual payment 

Semi-annual payment =$4176.157=\$4176.157

Total payment = Semi-annual payment x number of payments 

Total payment =10×4176.157=41761.57=10 × 4176.157=41761.57

Total payment =$41761.57=\$41761.57

b)

Interest=Total paymentloan amountInterest=41761.5736550Interest=$5211.57Interest =Total \space payment- loan \space amount \\ Interest =41761.57 - 36550\\ Interest =\$5211.57\\


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