Jack Jones wants to buy a one-way bus ticket to Kings Canyon.The ticket costs $142, but Jack has only $80.If Jack puts the money in an account that pays 9% interest compounded monthly, how many months must Jack 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 after time t, P is the principal (starting amount), r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

We want to solve for t, so we can rewrite the formula as:
t = (1/n) * log(A/P) / log(1 + r/n)

Plugging in the values given in the problem, we get:
P = $80
A = $142
r = 0.09 (9% as a decimal)
n = 12 (compounded monthly)

t = (1/12) * log(142/80) / log(1 + 0.09/12) = 76.85

Rounding to the nearest month, we get t = 77 months. Therefore, the answer is C) 77 months.

Jack Jones Wants to Buy a One-Way Bus Ticket to Kings