Question

Esteban bought a new stove for $986 on his credit card. He used the stove for eleven years before replacing it. The stove cost him an average of $0.14 per day in electricity. Esteban had preventive maintenance done on the stove, costing $24.25 each year for the eleven years. Esteban’s credit card has an APR of 9.26%, compounded monthly. He paid off his balance by making identical monthly payments for five years. Sales tax in Esteban’s area is 8.22%. Assuming that Esteban made no other purchases or payments with his credit card, what was the lifetime total cost of the stove? (Assume that two of the years Esteban had the stove were leap years, and round all dollar values to the nearest cent.)
a.
$2,534.57
b.
$2,166.53
c.
$2,234.23
d.
$2,064.53

Answer 1

Step 1 — Purchase with tax:
986 × (1 + 0.0822) = 986 × 1.0822 = $1,067.05 (rounded to the cent).

Step 2 — Monthly payment on the credit card:
Monthly rate r = 0.0926/12 = 0.0077166667. Number of payments n = 60.
Monthly payment = P·r / (1 − (1+r)^−n)
= 1,067.05·0.0077166667 / (1 − (1.0077166667)^−60)
≈ $22.29 per month (rounded to the cent).

Total paid on the card = $22.29 × 60 = $1,337.40.

Step 3 — Electricity and maintenance over 11 years:
Days = 9·365 + 2·366 = 4,017 days.
Electricity = 4,017 × $0.14 = $562.38.
Maintenance = $24.25 × 11 = $266.75.

Step 4 — Lifetime total cost:
1,337.40 + 562.38 + 266.75 = $2,166.53.

Answer: b. $2,166.53