Question

Xavier deposits $6 daily into an interest bearing account to save for renovations. The account earns 4.57% which compounds annually. What is the present value of the investment if Xavier renovates in five years?

Answer 1

To solve this, we are going to use the present value formula:
`PV=P[ (1-(1+ (r)/(n))^(-kt) )/( (r)/(n) ) ]`
where

`PV` is the present value

`P` is the periodic payment

`n` is the number of times the interest is compounded per year
`k` is the number of payments per year
`t` is the number of years
We know for our problem that Xavier deposits $6 daily into an interest bearing account, so
`P=6` and
`k=365`. To convert the interest rate to decimal form, we are going to divide the rate by 100%

`r= (4.57)/(100) =0.0457`
Since the interest is compounded annually, it is compounded 1 time per year; therefore,
`n=1`. We also know that Xavier renovates in five years, so
Lets replace the values in our formula:

`PV=P[ (1-(1+ (r)/(n))^(-kt) )/( (r)/(n) ) ]`

`PV=6[ (1-(1+ (0.0457)/(1))^(-(365)(5)) )/( (0.0457)/(1) ) ]`

`PV=131.29`

We can conclude that the present value of Xavier's investment is $131.29