Question

Sean invests $7,500 in an account that pays 1.4% annual interest, compounded

continuously. What is the balance, to the nearest cent, at the end of the 7 years?

Answer 1

$8,266.60

Explanation:

Account at the start: $7, 500

Account after first year: (7, 500 X 1.4%) + 7,500 = 7,605

(lets rewrite the above equation)

Account after first year: 7,500 [ (1 x 1.4%) + 1] = 7,500 (1.4% + 1)

= 7,500 X 1.014

Account after second year: (7, 500 X 1.014) X 1.014 [cus compounded annually]

(lets rewrite the above equation)

Account after second year: (7, 500 X 1.014) X 1.014 = 7500 X 1.014 X 1.014

Now lets compare the equations for " Account after first year" and " Account after Second year":

Account after first year: 7,500 X 1.014

Account after second year: 7500 X 1.014 X 1.014

The pattern we observe is that the 1.014 appear X number of times in the equation for X number of years:

for example: when the number of year is 2, number of times X appears is 2 time -->7500 X 1.014 X 1.014

So, we can conclude that the account after the end of 7 years is:

7,500 X 1.014 X 1.014 X 1.014 X 1.014 X 1.014 X 1.014 X 1.014

or

7 500 X (1.014^7) [understanding is (1.014 to the power of 7 )

And the final answer is: $8266.60 (nearest cent