Use economic equivalence to determine the amount of money or value of i that makes the following statements correct.

Question

(a) $5000 today is equivalent to $4275 exactly 1 year ago at i = ___% per year.
(b) A car that costs $28,000 today will cost $____ a year from now at i = 4% per year.
(c) At i = 4% per year, a car that costs $28,000 now, would have cost $____ one year ago.
(d) Last year, Jackson borrowed $20,000 to buy a preowned boat. He repaid the principal of the loan plus $2750 interest after only 1 year. This year, his brother Henri borrowed $15,000 to buy a car and expects to pay it off in only 1 year plus interest of $2295. The rate that each brother paid for his loan is ___ % for Jackson and ___ % per year for Henri.
(e) Last year, Sheila turned down a job that paid $75,000 per year. This year, she accepted one that pays $81,000 per year. The salaries are equivalent at i = ____% per year.

Answer 1

(a) i = (5000-4275)/4275 = 0.17 (17%)
(c) Price one year later = 28,000 * 1.04 = $29,120
(d) Price one year earlier = 28,000/1.04 = $26,923
(e) Jackson: Interest rate = (2750/20,000)*100
= 13.75%

Henri: Interest rate = (2295/15,000)*100
= 15.30%

(f) 81,000 = 75,000 + 75,000(i)
i = 6,000/75,000
= 0.08 (8%)