AV Convert to PictureA SmartArt CHAPTER 6 APR versus Period

AV - Convert to PictureA SmartArt CHAPTER 6 APR versus Period Rate APR= PERIOD RATE\" NO, OF PERIODS PER YEAR . Choice A: $755 end-of-month payments invested for three years if the money is compounded at 5% every month. Choice B: Lump-sum investment also good for three years with 14.0 percent compounded annually. . How much would you need to invest in B today for it to be worth as much as investment A three years from now? y including the compounding for better understanding the problem. Notes CommentsE:: B.

Solution

Choice A:

Monthly Payment = $755
Annual Interest Rate = 5%
Monthly Interest Rate = 0.4167%
Period = 3 years or 36 months

Future Value = $755*1.004167^35 + $755*1.004167^34 + ... + $755*1.004167 + $755
Future Value = $755 * (1.004167^36 - 1) / 0.004167
Future Value = $755 * 38.75357
Future Value = $29,258.95

Choice B:

Annual Interest Rate = 14%

Initial Deposit * 1.14^3 = $29,258.95
Initial Deposit * 1.481544 = $29,258.95
Initial Deposit = $19,748.96

So, you need to invest $19,748.96 today in B to have same value as A after 3 years