Question

A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.

Answer 1

Explanation:

y = 1000(1+0.04)^20

y = 1000(1.04)^20

Rounded to the nearest hundredth

y = 1000(2.19)

y = $2190

Answer 2

The current value of the stamp collection is of $2,191.

Explanation:

Compound interest:

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 year and t is the time in years for which the money is invested or borrowed.

A stamp collection is purchased for $1,000.

This means that
`P = 1000`

The rate of return on the stamp collection is 4% per year

This means that
`n = 1, r = 0.04`

So

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

`A(t) = 1000(1 + 0.04)^(t)`

`A(t) = 1000(1.04)^(t)`

What is the current value of the stamp collection?

This is A(20). So

`A(20) = 1000(1.04)^(20) = 2191`

The current value of the stamp collection is of $2,191.