Question

Clementine and Leeexpect to deposit the following cash flows at the end of years 1 through 5, $1,000; $4,000; $9,000; $5,000; and $2,000 respectively. Alternatively, theycould deposit a single amount todayand have the same amount in your account at the endof year 5. How large does the single deposit need to be today if Clementine and Leecan earn 10% compounded annuallyon their account?

Answer 1

The single deposit value will be "$15,633.62".

Step-by-step explanation:

According to the question, the future values will be:

=
`(1000* ((1+10 \ percent)^4)+(4000* ((1+10 \ percent)^3)+(9000* ((1+10 \ percent)^2)+(5000* ((1+10 \ percent))+2000`

=
`1464.1+5324+10890+5500+2000`

=
`25178.1`

By using the Present value formula, the single deposit will be:

⇒
`Present \ value=(Future \ value)/((1+Interest \ rate)^n)`

`=(25178.1)/((1+10 \ percent)^5)`

`= (25178.1)/(1.61051)`

`=15,633.62` ($)