Question

Simon recently received a credit card with an 20% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $500. The minimum payment on the card is only $20 per month.

If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest month.
month(s)

If Simon makes monthly payments of $60, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest month.
month(s)

How much more in total payments will Simon make under the $20-a-month plan than under the $60-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

REACHING A FINANCIAL GOAL

Six years from today you need $10,000. You plan to deposit $1,600 annually, with the first payment to be made a year from today, in an account that pays 6% effective annual rate. Your last deposit, which will occur at the end of Year 6, will be for less than $1,600 if less is needed to reach $10,000. How large will your last payment be? Round your answer to the nearest cent.

Answer 1

If Simon makes $ 20 payment per month

PMT = PV of loan / 1 - ( 1+interest rate)^-nt / interest rate

$ 20 = $ 500 1 - [ (1 + ( 0.20/12))^-12t ( 0.20/12)

Solving for t

T = 33 months

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If Simon makes monthly payments of $60

$ 60 = $ 500 1 - [ (1 + ( 0.20/12))^-12t ( 0.20/12)

Solving for t

T = 9 months

Total payments if $ 20 is paid per month = $ 20 * 33 ( $ 660)

Total payments if $ 60 is paid per month = $ 60 * 9 ( $ 540)

More in total payments = $ 660- $ 540

More in total payments = $ 120

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The future value at end of 5 years

FV = $ 1600 [ (1+0.06)⁵   - 1 ] 0.06

FV = $ 9,019.35

The balance needed to reach $ 10,000 is = $ 10,000 - $ 9,019.35

Balance needed = $ 980.65

Last payment = $ 980.65 ( 1+0.06)¹

Last payment = $ 925.14