Question

An engineer borrowed $3000 from the bank, payablein six equal end-of-year payments at 8%. The bankagreed to reduce the interest on the loan if interestrates declined in the United States before the loanwas fully repaid. At the end of 3 years, at the timeof the third payment, the bank agreed to reduce theinterest rate from 8% to 7% on the remaining debt.What was the amount of the equal annual end-of-year

payments for each of the first 3 years? What was theamount of the equal annual end-of-year payments foreach of the last 3 years?

Answer 1

ANSWER:

End of year payment for the first 3 years = borrowed amount(a/p,i,n) = 3,000(a/p,8%,6) = 3,000 * 0.2163 = 648.95

now we will find the future value of the borrowed amount and end of year payment for the first 3 years after 3 years.

fv of borrowed aount after 3 years = borrowed amount(f/p,i,n) = 3,000(f/p,8%,3) = 3,000 * 1.2597 = 3,779.14

fv of end of year payment for first 3 years after 3 years = 648.95(f/a,8%,3) = 648.95 * 3.2464 = 2,106.74

amount left after 3 years = fv of borrowed aount after 3 years - fv of end of year payment for first 3 years after 3 years = 3,779.14 - 2,106.74 = 1,672.40

end of year payments for the last 3 years = amount left after 3 years(a/p,i,n) = 1,672.40(A/p,7%,3) = 1,672.40 * 0.3811 = 637.27

so the end of year payments for 1st 3 years is $648.95 while for the last 3 years end of year payments is $637.27