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

Answer:

8.82 years.

Step-by-step explanation:

Since, the monthly payment formula is,

$P=\frac{PV(r)}{1-(1+r)^{-n}}$

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 = $\frac{0.052}{12}$

( 1 year = 12 months )

P = $ 295,

By substituting the values,

$295=\frac{25000(\frac{0.052}{12})}{1-(1+\frac{0.052}{12})^{-n}}$

By the graphing calculator,

We get,

$n = 105.84$

Hence, the time ( in years ) = $\frac{105.84}{12}=8.82$