Question

Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $295 monthly at 5.2% to accumulate $25,000.

Answer 1

8.82 years.

Explanation:

Since, the monthly payment formula is,

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

Where, PV is the present value of the loan,

r is the rate per month,

n is number of months,

Here,

PV = $ 25,000,

Annual rate = 5.2 % = 0.052 ⇒ Monthly rate, r =
`(0.052)/(12)`

( 1 year = 12 months )

P = $ 295,

By substituting the values,

`295=(25000((0.052)/(12)))/(1-(1+(0.052)/(12))^(-n))`

By the graphing calculator,

We get,

`n = 105.84`

Hence, the time ( in years ) =
`(105.84)/(12)=8.82`