Question

Lab Exercises D Your grandfather gave you $50,000. You want to set aside some of that money so you can withdraw $900/month for living expenses for the 4 years you attend university and still have $7,000 left at the end of the 4 years to pay for a trip after graduation. Your first withdrawal will be in one year when you start university. Assume you earn j12 4% the entire time. (a) How much of the $50,000 must you set aside? (b) How much interest will you earn?

Answer 1

Answer (a):

Total amount now = $50,000

After one year amount to be withdrawn monthly at the start of month for 4 years = $900 per month

Amount required at the end 4 years (from start of month attending university) = $7,000

Monthly Interest rate (compounded monthly) = 4%/12

Number of months = 48

Let us first calculated amount required (PV) after one year from now:

= PV(rate, nper, pmt, fv,type)

= PV (4%/12, 48, -900, -7000, 1)

= $45959.411

Amount required after one year = $45,959.411

Amount required now = PV = FV / (1 + Periodic interest) ^{Number of periods}

= 45959.411 / (1 + 4%/ 12) ¹²

= $44,160.25

Amount you need to set aside = $44,160.25

Answer (b):

Interest earned = Total amount withdrawn + Balance left in account - Amount set aside

= 900 * 48 + 7000 - 44160.25

= $6039.75

Interest you will earn = $6,039.75