Question

Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years&

A. 5(0.08x)
B. 5(1.08x)
C. {1+5(0.08)}x
D. (1.08)^5 *(x)
E. (1.08x)^5

Answer 1

D.

Step-by-step explanation:

`x*1.08^(5)`.

the key for answering this question is the word "Compounded". there are different ways to calculate interest, the compounded one is characterized for adding interest to capital, so you earn interest over interest for each perdiod the interest of the prior one is added to the principal, so every year you multiply the interest plus the capital invested it is as follows:

`x*(1+i)*(1+i)*(1+i)*(1+i).....`

note that i is the interest as in this case 0.08, and x is the invested value, so for every year of the investment is necessary to multyply by
`(1+i)` that's why at the end of the 5 years you have
`(1+i)^(5)`