Question

Periods Future Value of 1 at 8%

1 1.080
2 1.166
3 1.260
4 1.360
5 1.469
What amount will be in a bank account three years from now if $10,000 is invested each year for four years with the first investment to be made today?
a. ($10,000 × 1.260) + ($10,000 × 1.166) + ($10,000 × 1.080) + $10,000
b. $10,000 × 1.360 × 4
c. ($10,000 × 1.080) + ($10,000 × 1.166) + ($10,000 × 1.260) + ($10,000 × 1.360)
d. $10,000 × 1.080 × 4

Answer 1

The correct answer is a), representing the sum of each annual $10,000 investment grown at a compound rate of 8% for different periods, with the first investment made immediately and the last at the end of the four-year term.

Step-by-step explanation:

The question involves calculating the future value of a series of investments in the context of compound interest. This is a fundamental concept in financial mathematics, where amounts invested today grow at a certain rate over a period of time. In this scenario, the first investment is made today and grows for four years. The second investment is made a year from today and grows for three years, and this pattern continues with subsequent investments.

The correct answer to the question is option a), which can be understood using the following formula:

• The first $10,000 investment grows for three years: $10,000 × 1.260
• The second $10,000 investment grows for two years: $10,000 × 1.166
• The third $10,000 investment grows for one year: $10,000 × 1.080
• The fourth $10,000 investment is made at the end of the period: $10,000

So, the total future value will be the sum of these individual amounts.