Question

Assuming a 4% (0.04) interest rate, $300 invested today in a savings account today will be worth $312 in one year. What will that amount be in 2 and 3 years, and what is the total interest you will earn at the end of three years.

Answer 1

in 2 years the savings account will show: $324.48

in 3 years the savings account will show: $337.46

so the interest earned in these three years would be $337.46 - $300 = $37.46

Explanation:

The equation for interest rate compounded annually is what describes this investment, since:
`A=P(1+r)^t` where A is the accrued value (total value of principal plus accumulated interest) in the account after the first year ($312), P the principal ($300 in our case), and r the interest rate in decimal form (0.04), and t is the time in years (one for the fist year). They perfectly satisfy the equation:

`A=P(1+r)^t\\312=300(1+0.04)^1\\312=312`

Then, we can apply this equation for years 2 and 3, just changing the value of t to 2 and 3, as shown below:

`A=P(1+r)^t\\A=300(1+0.04)^2\\312=324.48\\A=300(1+0.04)^3\\312=337.4592`

We can round the last value to two decimals (cents) obtaining: $337.46

The pure interest after the three years is therefore the total at that time minus the principal the account was started with ($300): $337.46 - $300 = $37.46