Intrest, money, algebra

Question

Gretchen deposited $7000 in an account that earns 2% interest compounded annually..

(a) Write an equation that expresses the amount of money in the account as a function of n, where n equals the number of years since the original deposit was made.

(b) Use the equation in (a) and a calculator to determine how much money will be in the account after 6 years.

(c) How much interest will have been earned after 6 years?

Answer 1

2% interest means, if you have $1, then at the end of the first year you will get $ 0.02 as interest, so the total amount at the end of one year is 1 + 0.02 = $ 1.02.

Which means since he initially deposits $7000 dollars, at the end of year 1, he'll have 7000×(1.02) dollars.

The starting amount at year 2 will then be 7000×(1.02) dollars, so he'll have 7000×(1.02)×(1.02) = 7000×(1.02)² dollars at the end of 2nd year. Likewise, at the end of 3rd year he'll have 7000×(1.02)3 dollars. You see the pattern. At the end of n years, he'll have 7000×(1.02)ⁿ dollars. So,

(a) 7000×(1.02)ⁿ

(b) Plug in n = 6, 7000 * (1.02)⁶ = $ 7883.14

(c) So the interest is the what you have extra off $7000. So interest = 7883.14 - 7000.00 = $ 883.14