Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased an Amazon Kindle for $350. The minimum payment on the card is only $10 per month a. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card. Round to the nearest month.
b. If Simon makes monthly payment of $30, how many months will it be before he pays off the card. Round to the nearest month.
c. How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan? Make sure you use three decimal places for N.

A.50 months

B.12.92 months

C.$112.38

Explanation:

a). Using this formula

PV of Annuity = Monthly Payment * [{1 - (1 + r)-n} / r]

Where,

PV of Annuity =$350

Monthly Payment =$10

r=(0.18/12)

Let plug in the formula

$350 = $10 * [{1 - (1 + 0.18/12)-n} / (0.18/12)]

$350 / $10 = {1 - (1.015)-n} / 0.015

35 * 0.015 = 1 - (1.015)-n

(1.015)-n = 1 - 0.525

-n[log(1.015)] = log(0.475)

-n[0.0149] = -0.7444

n = -0.7444 / -0.0149

n= 50 months

b). Using this formula

PV of Annuity = Monthly Payment * [{1 - (1 + r)-n} / r]

Where,

PV of Annuity =$350

Monthly Payment =$30

r=(0.18/12)

Let plug in the formula

$350 = $30 * [{1 - (1 + 0.18/12)-n} / (0.18/12)]

$350 / $30 = {1 - (1.015)-n} / 0.015

11.67 * 0.015 = 1 - (1.015)-n

(1.015)-n = 1 - 0.175

-n[log(1.015)] = log(0.825)

-n[0.0149] = -0.1924

n = -0.1924 / -0.0149 =

n=12.92 months

c). Calculation for the Total Amount Paid under $10-a-month plan

Using this formula

Total Amount Paid under $10-a-month plan = No. of Payments * Monthly Payment

Where,

No.of Payments =50

Monthly Payment=10

Let plug in the formula

Total Amount Paid under $10-a-month plan= 50 * $10 = $500

Calculation for the Total Amount Paid under $30-a-month plan

Using this formula

Total Amount Paid under $30-a-month plan = No. of Payments * Monthly Payment

Where,

No. of Payments =12.92

Monthly Payment=$30

Let plug in the formula

Total Amount Paid under $30-a-month plan= 12.92 * $30 = $387.62

Hence,

Total Amount Paid under $10-a-month plan -Total Amount Paid under $30-a-month plan

= $500 - $387.62

= $112.38

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