Clara is setting up a retirement fund,and she plans on depositing $5,000 per year in an investment that will pay 7% annual interest.How long will it take her to reach her retirement goal of $69,082? (PV of $1,FV of $1,PVA of $1,and FVA of $1)(Use appropriate factor(s)from the tables provided.)
A)13.816 years
B)0.072 years
C)10 years
D)20 years
E)5 years

Question

Quizplus · Accepted Answer

We can solve this problem using the formula for the future value of an annuity:

FV = A x ((1 + r)^n - 1) / r

where:
A = annual deposit
r = interest rate
n = number of years

Substituting the given values, we get:

$69,082 = $5,000 x ((1 + 0.07)^n - 1) / 0.07

Simplifying and solving for n, we get:

n = log(1 + ($69,082 x 0.07 / $5,000)) / log(1 + 0.07)

Using the calculator or logarithm tables, we get:

n = 10.00 years (rounded to two decimal places)

Therefore, it will take Clara 10 years to reach her retirement goal of $69,082 by depositing $5,000 per year at 7% annual interest. Using the formula for Future Value of an Annuity (FVA):
FVA = Pmt x [(1 + r)^n - 1] / r

Where:
Pmt = $5,000 (the annual deposit)
r = 7% (the annual interest rate)
FVA = $69,082 (the retirement goal)

Plugging in the values:
$69,082 = $5,000 x [(1 + 0.07)^n - 1] / 0.07

Solving for n:
n = 10.042 years

Therefore, it will take Clara 10 years to reach her retirement goal. The closest option is C) 10 years.

Clara Is Setting Up a Retirement Fund,and She Plans on Depositing