Your credit card balance is $8200 with 18% APR. You decide to pay it off over 2

Question

Your credit card balance is $8200 with 18% APR. You decide to pay it off over 2 years of equal monthly payments . A. How large should your monthly payments be? B. What is the interest portion of the 19th payment? C. what would your lean balance be immediately after you make your 20th payment? You have decided to set up a trust fund for your heirs that will allow them to received $30,0000 each year forever with the first payment to be received in 8 years. You found an investing that will return 3% on your investing. How much should you invest invest today to achieve this goal?

Explanation / Answer

1) CREDIT CARD:

A) The monthly payments would be an annuity, the PV of which annuity would be the balance of $8200.

Therefore 8200 = PMT*pvifa(18/12,24); 8200 = PMT*20.0304

PMT(monthly payments) = $409.38

B) Interest portion of the 19th payment:

= loan balance after the 18th payment * 1.5%

loan balance after the 18th payment would be the PV of the last 6 instalments

Therefore interest portion of the 19th payment = 409.38*pvifa(1.5,6)*0.015 = 409.38*5.6972*0.015 = $34.98

C) Loan balance after 20th payment = PV of balance 4 instalments = 409.38*pvifa(1.5,4) = 409.38*3.8544 = $1577.91

2) TRUST FUND:

The amount to be built up by the end of the seventh year would be the PV of the perpetuity of $30,000, which would be = 30000/0.03 = 1,000,000.

This will be the FV of the amount to be deposited today. The amount to be deposited today = 1,000,000/1.03^7 =

$813,092

Note: If the annual amount to be received is $300000, the answer would be $8,130,915.

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