Question

Hannah invested 35,000 in a mutal fund that earns 6% interest per annum compounded annually. To the nearest dollar, how much was her investment worth after 3 years?Answers:1. 39,2002. 39,3263.41,3004.41,686

Answer 1

Compounded interest

Compounded interest takes into account all the accumulated interest of previous periods.

We have that it is the described by the following formula:

`A=P(1+(r)/(n))^(nt)`

where,

A = the future value of the investment, including interest

P = the initial investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the time the money is invested

In this question:

A = what we want to find

P = 35,000

r = 0.06 (since it is 6%, we divide 6/100 = 0.006)

n = 1 (since it is per annum)

t = 3 (since we want to find it after 3 years)

Now, we replace in our formula:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \downarrow \\ A=35,000(1+(0.06)/(1))^(1\cdot3) \\ \downarrow \\ A=35,000(1+0.06)^3 \\ A=35,000(1.06)^3 \\ \downarrow \\ (1.06)^3\approx1.191 \\ A\approx35,000\cdot1.191 \\ A\approx41,685 \end{gathered}`

Answer: 4