You need to take out a loan for 15000 and want to repay as p

You need to take out a loan for $15,000 and want to repay as possible. Which bank should you take the loan from? Bank A: offers a 10-year loan, at 4.5% interest, simple interest. offers a 10-year loan at 5% interest compounded continuously.

Solution

Bank A offers a 10 year loan at a simple interest of 4.5% p.a. The formula for simple interest is F = P(1+rt), where P is the principal or the initial amount borrowed, F is the amount to be repaid, r is the rate of interest in decimals and t is the period of loan. Then F = 15000(1 + 0.045*10) = 15000(1+ 0.45) = 15000(1.45 ) = $21750.

Bank B offers a 9 year loan at 5.5% compounded quarterly. The formula for compound interest is F = P(1+r)^t where P is the principal or the initial amount borrowed, F is the amount to be repaid, r is the rate of interest for the period in decimals and t is the period of loan. Here, P= $ 15000, r = (5.5/100)(1/4) = 0.01375 and t = 9*4 = 36. Then, F = 15000(1+ 0.01375)³⁶ = 15000(1.01375)³⁶ = 15000*1.63497539= $24524.63

Bank C offers a 10 year loan at 5 % interest compounded continuously. The formula for contious compounding is F = Pe^rt where P is the principal or the initial amount borrowed, F is the amount to be repaid, r is the rate of interest for the period in decimals and t is the period of loan. Here, P= $ 15000, r = 5/100 = 0.05 and t = 10. Then F = 15000e^0.5 = 15000*1.64872127= $ 24730.82

Thus, one has to repay the least when the borrowing is from Bank A.Thus, it is advisable to take the loan from Bank A.