Question

1) Immer and Mays are both saving for retirement in 35 years. Immer starts immediately and deposits $175.00 per month into a retirement account with an interest rate of 6% which is compounded annually. Mays waits for 15 years before she starts depositing money in her retirement account at 6% compounded annually. How much money will Mays need to deposit into her account each month to end up with the same amount of savings as Immer when they both retire?

2) Hadi has found a car he would like to purchase and he needs to finance $15,000 of the sticker price to buy this car. He can afford no more than $282/month for payments over 5 years. What annual percentage rate (APR) will make it possible for him to afford this car?

Answer 1

Part A First of all, we will calculate the total amount saved by Immer for his retirement life Immers monthly saving Annual savings (Monthly savings X 12) Annual compounding interest rate Period 175 2100 6% 35 years Following formula is being used in excel to calcuate return amount when interest rate is annual compounding and study annual payments made. Future value= FV(rate,nper,pmt, [pv],[type]) Where, Rate nper (Investment period) pmt (Annual payments) [pv] 6% 35 2100 This is present value which is by defalut taken as [type] Under this option we have to put 1 since payments are made in the begning of each month By putting values in the formula we get that total Savings made by immers for retirement FV(6%,35,-2100,0,1) $248,053.82 So total Savings required to mays at retirement is also Period Rate $248,053.82 20 years 6% Following formula is being used in excel to calcuate investment amount when interest rate is annual compounding. Insatallement amount PMT(rate,nper, pv,[fv], [type]) Where, Rate nper (Investment period) pv [fv] [type] 6% 35 This amount will be taken as 0 Required future value Under this option we have to put 1 since payments are made in the begning of each month PMT(6%,20,0,-248053.82,1) By putting values in the formula we get that total annually following amount is required to be saved by mays Savings made by immers for retirement=6361.54 or monthly $530.13 Part B To calculate the annual percentage rate following formula is being used in excel APR Rate(nper,pmt,pv, [fv],[type]) Where, nper (Investment period) pmt pv [fv] [type] annual payments this will be 0 15000 Under this option we have to put 1 since payments are made in the begning of each month RATE(5,3384,0,-15000,1) By putting values in the formula we get that total annually following amount is required to be saved by mays Savings made by immers for retirement -3.988% Maximum APR that can be afforded by him is -3.988% or 4%