Glen wants to take a holiday that costs $8,850, but currently he only has $2,750 saved. If he invests this money at 8 percent interest compounded annually, how long will he have to wait to take his holiday?
A)12.36 years
B)16.25 years
C)15.19 years
D)13.52 years
E)14.12 years

Question

Quizplus · Accepted Answer

We can use the formula A=P(1+r/n)^nt where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years. Rearranging the formula to solve for t, we have t=(ln(A/P))/(n*ln(1+r/n)). Substituting the given values, we have A=8850+2750=11600, P=2750, r=0.08, n=1 (compounded annually). Plugging these into the formula, we get t=(ln(11600/2750))/(1*ln(1+0.08/1))=15.19 years. Therefore, the answer is C.

Glen Wants to Take a Holiday That Costs $8,850, but Currently