Question

Simon recently received a credit card with a 12% nominal interest rate. With the card, he purchased an Apple iPhone 7 for $384.15. The minimum payment on the card is only $10 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 whole number.

If Simon makes monthly payments of $35, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest whole number.

How much more in total payments will Simon make under the $10-a-month plan than under the $35-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The formula that can be used to solve this is:

t = (log (1 - (PV * (r/n)/PMT)) / (-n*log(1+ (r/n)))

Where,

PMT - Annuity payments

r - nominal interest rate

n - periods per year

t - number of years

Taking the first situation, we have the following information:

PV - $384.15

Annuity payments - $10

Interest rate - 12%

Periods/year - 12

thus, t = (log( 1 - (384.15 * (0.12/12) / 10) ) / -12 log (1 + 0.12/12)

t = log ( 1 - 0.38415) / -12 log ( 1.01)

t = log (0.61585) / -12 * 0.0043214

t = -0.210525/ - 0.05186

t = 4.05949 years

Answer - 4.05949 years or 4 years

Taking the second situation, we have the following information:

PV - $384.15

Annuity payments - $35

Interest rate - 12%

Periods/year - 12

thus, t = (log( 1 - (384.15 * (0.12/12) / 35) ) / -12 log (1 + 0.12/12)

t = log ( 1 - 0.109757) / -12 log ( 1.01)

t = log (0.890243) / -12 * 0.0043214

t = -0.050491/ - 0.05186

t = 0.9736 years

Answer - 0.9736 years or 1 year

To find the difference in both the plans:

Plan 1:

No. of payments = 12*4.05949 = 48.714$

Monthly payments = 10$

Total payment = 487.14$

Plan 2:

No. of payments = 12*0.9736 = 11.683$

Monthly payments = 35$

Total payment = 408.912$

Difference is 78.23 dollars and the 10$ plan is higher.