Question

Your Uncle Bob has arranged a loan at the Bank for $1,000 which he will repay in 10 equal annual payments at a 10% interest rate. Immediately after his 3rd payment, he calls the banker to enquire about borrowing another $500. He tells the banker that he can’t afford for the payment to go up too dramatically and he offers to let him repay the remaining debt on the original loan plus the new $500 loan in 12 equal annual payments. The first payment will be at the end of one year and the interest rate is unchanged at10%. Bob says he will think about it and then comes to you asking if you can tell him how much his new payment will be. What is the amount of the 12 new payments?

Answer 1

Annual installment in case of first loan will be :

= Loan amout/PVIFA(10%,10 years)

1000/6.145

= $162.73

Computation of principle amount repaid in 3 years:

end of 1st year = Installment amount - interest amount

= 162.73 - (1000*10%)

= $ 62.73

end of 2nd year = 162.73 - [(1000-62.73)*10%]

= $ 69

end of 3rd year = 162.73 - [(1000-62.73-69)*10%]

= $ 75.90

Hence the remaining principle amount after 3rd installemnt = $792.37

Additional loan taken = $500

total loan amount = $ 1292.37

Annual installment amount = loan amount/PVIFA(10%,12 years)

= 1292.37/6.814

=$189.66 (approx)