Question

You want to have $10,000 in 5 years to purchase a car. How much would you have to invest today (in the present time) to have $10,000 five years in the future if you invested at 6% (assume the present value of a single amount for 5 years at 6% is 0.747)?

Answer 1

$ 7470

Step-by-step explanation:

Given,

The present value of a single amount for 5 years at 6% is 0.747,

That is,

The ratio of present value and future value is
`(0.747)/(1)`

Let x be the present value that would be invested at 6% interest for 5 years for the future value of $ 10,000

Then the ratio of present value and future value is
`(x)/(10000)`

`\implies (x)/(10000)=(0.747)/(1)`

`\implies x=7470`

Hence, the present value would be $ 7,470.

Alternative method :

Future value formula,

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

Where,

P = invested amount, r = rate per period ( in decimals ), t = number of periods,

Here, A = 10,000, r = 6% = 0.06, t = 5,

`10000=P(1+0.06)^5`

`\implies P=\$ 7472.58`

Which is nearby $ 7,470.