Question

1. An investment of $2000 earns 5.75% interest, which is compounded quarterly. After

approximately how many years will the investment be worth $3000?

Answer 1

After 7.1 years

Explanation:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

We have to find t, for which
`A(t) = 3000` when
`P = 2000, r = 0.0575, n = 4`

So

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

`3000 = 2000(1 + (0.0575)/(4))^(4t)`

`(1.014375)^(4t) = (3000)/(2000)`

`(1.014375)^(4t) = 1.5`

`\log{(1.014375)^(4t)} = \log{1.5}`

`4t\log{1.014375} = \log{1.5}`

`t = \frac{\log{1.5}}{4\log{1.014375}}`

`t = 7.1`

After 7.1 years

Answer 2

Two years investment will bring about $3,000

Explanation:

Kindly check the attached picture for the workings.