Given below are the future value factors for 1 at 8% for one to five periods. Each of the items 48 to 51 is based on 8% interest compounded annually.

-If $3,000 is put in a savings account today, what amount will be available three years from today?
A)$3,000 ÷ 1.260
B)$3,000 × 1.260
C)$3,000 × 1.080 × 3
D)($3,000 × 1.080) + ($3,000 × 1.166) + ($3,000 × 1.260)

Question

Given below are the future value factors for 1 at 8% for one to five periods. Each of the items 48 to 51 is based on 8% interest compounded annually.

-If $3,000 is put in a savings account today, what amount will be available three years from today?
A)$3,000 ÷ 1.260 
B)$3,000 × 1.260 
C)$3,000 × 1.080 × 3 
D)($3,000 × 1.080) + ($3,000 × 1.166) + ($3,000 × 1.260)

Quizplus · Accepted Answer

The most likely scenario is that the question is asking for the future value of $3,000 after 3 years with interest ($	ext{FV}$). We can use the formula $	ext{FV}=	ext{PV}	imes(1+r)^n$ where $	ext{PV}$ is the present value (the initial investment), $r$ is the annual interest rate, and $n$ is the number of years.

However, we are not given the interest rate, so we need to make an assumption. Since none of the answer choices suggest using a formula with interest and we are not provided with any other information, we can assume that the interest is compounded annually and that the interest rate is constant over the 3 years.

Out of the answer choices given, only choice B provides a formula that takes into account an interest rate and compounding, so we can select it as the answer. We can solve for the interest rate as follows:

$	ext{FV}=	ext{PV}	imes(1+r)^n$
$\dfrac{	ext{FV}}{	ext{PV}}=(1+r)^n$
$\sqrt[n]{\dfrac{	ext{FV}}{	ext{PV}}}=1+r$
$r=\sqrt[n]{\dfrac{	ext{FV}}{	ext{PV}}}-1$

If we assume an interest rate of 6% (or 0.06 in decimal form), then the formula becomes:

$	ext{FV}=	ext{PV}	imes(1+0.06)^3 = 3000	imes1.191 = 3573$

This is close to choice B: $3,000	imes1.260=3780$, which suggests an interest rate of about 5.33% (approximately $\sqrt[3]{1.260}-1$). Although this does not exactly match our assumed interest rate, it is the answer choice that makes the most sense based on the information given.

Given Below Are the Future Value Factors for 1 at 8