The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations.
- Approximately how many years will it take for a sum invested at 8% with annual compounding to quadruple?
A)9 years
B)17 years
C)18 years
D)81 years

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for future value with annual compounding:

FV = PV × (1 + r)n

where PV is the present value, r is the annual interest rate, and n is the number of years.

We want to find out when the sum invested will quadruple, which means that the future value (FV) will be 4 times the present value (PV):

FV = 4 × PV

Substituting this into the formula above, we get:

4 × PV = PV × (1 + 0.08)n

Dividing both sides by PV and simplifying, we get:

4 = (1 + 0.08)n

Using logarithms, we can solve for n:

n = log(4) / log(1 + 0.08)
n ≈ 17 years

Therefore, the answer is C: 18 years (rounded up from 17.67 years).

The Solution to This Problem Requires Time Value of Money