Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month)?
A) 73 months
B) 75 months
C) 77 months
D) 79 months

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
We want to find t when A = $142, P = $80, r = 9% = 0.09, and n = 12 (monthly compounding).
142 = 80(1 + 0.09/12)^(12t)
1.775 = (1.0075)^(12t)
Take the natural logarithm of both sides:
ln(1.775) = ln(1.0075)^(12t)
ln(1.775) = 12t ln(1.0075)
t = ln(1.775) / (12 ln(1.0075)) ≈ 76.7
Round to the nearest month, t ≈ 77. Therefore, Shorty needs to wait 77 months to have enough money for the bus ticket. The correct answer is (C) 77 months.

Shorty Jones Wants to Buy a One-Way Bus Ticket to Mule-Snort