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.
Accepted Solution
A:
Answer:8.82 years.Step-by-step explanation:Since, the monthly payment formula is,[tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]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 = [tex]\frac{0.052}{12}[/tex]( 1 year = 12 months )P = $ 295,By substituting the values,[tex]295=\frac{25000(\frac{0.052}{12})}{1-(1+\frac{0.052}{12})^{-n}}[/tex]By the graphing calculator,We get,[tex]n = 105.84[/tex]Hence, the time ( in years ) = [tex]\frac{105.84}{12}=8.82[/tex]