Question

You would like to have $10,000 in an account after eight years time. If the account earns 2.5% compounded interest yearly, how much would you have to deposit today

Answer 1

You have to deposit $8,207.5 today.

Explanation:

Compound interest:

The amount of money in yearly compounded interest, after t years, is given by the following equation:

`A(t) = A(0)(1+r)^t`

In which A(0) is the initial deposit and r is the interest rate, as a decimal.

You would like to have $10,000 in an account after eight years time.

This means that when
`t = 8, A(t) = 10000`

2.5% compounded interest

This means that
`r = 0.025`

So

`A(t) = A(0)(1+r)^t`

`A(t) = A(0)(1+0.025)^t`

`A(t) = A(0)(1.025)^t`

How much would you have to deposit today?

We have to find A(0), when
`t = 8, A(t) = 10000`. So

`A(t) = A(0)(1.025)^t`

`10000 = A(0)(1.025)^8`

`A(0) = (10000)/((1.025)^8)`

`A(0) = 8207.5`

You have to deposit $8,207.5 today.