Problem 5-36. Nonannual compounding a. You plan to make 3 deposits of $1,000 eac
ID: 2664368 • Letter: P
Question
Problem 5-36. Nonannual compoundinga. You plan to make 3 deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 5% nominal interest, compounded semiannually, how much would be in your account after 3 years?
Round your answer to the nearest cent.
b. One year from today you must make a payment of $6,000. To prepare for this payment, you plan to make 2 equal quarterly deposits, at the end of Quarters 1 and 2, in a bank that pays 5% nominal interest, compounded quarterly. How large must each of the 2 payments be?
Round your answer to the nearest cent.
Explanation / Answer
a) FV at t= 3rd semiannual period (= 1.5 years) = 1000(1.02^3 - 1)/0.02 = 3060.4 ($) (semi-annual rate = 4/2 = 2% = 0.02) FV of this at the end another 3 semi-annuals( at the end of year 3) = 3060.4(1.02)^3 = 3247.72 ($) (ANSWER) b) In this case, 14000 = a*((1+0.04/4)^2-1)/(0.04/4) * (1+0.04/4)^2 (WHERE a is payment at Q1 &Q2) => a = 6827.93 ($) (ANSWER)