Question

Suppose you invest $5,000 at 4% annual interest. How much money would your investment be worth after 10 years? Round your answer to the nearest hundredth (2 places after the decimal).

Answer 1

The investment will be worth $7,401.22 after 10 years

Here, we want to calculate the amount the investment will be worth after 10 years

Mathematically, to get this, we will use the compound interest formula;

`A\text{ = P(1 + }(r)/(n))^(nt)`

where A is the amount after 10 years

P is the amount invested which is $5,000

r is the interest rate which is 4%, same as 4/100 = 0.04

n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1

t is the number of years which is 10 in this case

Substituting these values, we have;

`\begin{gathered} A\text{ =5000 (1 + }(0.04)/(1))^(1*10) \\ \\ A=5000(1+0.04)^(10) \\ \\ A=5000(1.04)^(10) \\ \\ A\text{ = 7,401.22} \end{gathered}`