Question

​(Related to Checkpoint​ 5.2) ​(Future value) ​(Simple and compound​ interest) If you deposit ​$1 comma 000 today into an account earning an annual rate of return of 8 ​percent, in the third year how much interest would be​ earned? How much of the total is simple interest and how much results from compounding of​ interest?

Answer 1

Part A

Answer and its explanation:

Interest earned in the third year can be found from following two steps

Step 1 Use compounding formula for first two years, which is as under:

Future value = Present Value * (1+r)^n

Here n is the number of years the amount would be deposited for, which is 2 years duration. And r is the rate of return which is 8% here. So the future value in the year 2 will be:

Future value = $1000 * (1 + 0.08)^2 = $1166.4

Now the interest earned in the third year is:

Interest earned in the third year = $1166.4 * 8% = $93.312

Part B

Answer and its explanation:

The simple interest is the interest arising from the principal investment made in the year zero to date and this can be calculated as under:

Simple interest = Principal investment * rate of interest * number of years

Simple Interest = $1000 * 8% * 3years = $240

And the interest arising from the compounding of interest can be found by the difference of the Future value of the investment for three years and simple interest.

So,

Interest arising through compounding of interest = FV of investment in three years time - (Simple Interest + Principal investment)

Interest arising through compounding of interest = $1000*(1+0.08)^3 -$1240

= $19.712