Question

Use the sinking fund formula shown to the right to determine the monthly payment needed to accumulate $480,000 with 5% interest arecompounded monthly for 21 years.

Answer 1

Using the sinking fund formula and the information given, we have:

`\begin{gathered} P=(A)/((((1+(r)/(n))^(tn)-1)/((r)/(n))))\text{ } \\ A\colon\text{ Money accumulated( in this case \$480,000) } \\ \text{ P: Periodic contribution.} \\ r\colon\text{ Interest rate ( In this case 0.05)} \\ t\colon\text{ Number of years. (In this case 21 years)} \\ n\colon\text{ Number of payments per year (in this case 12)} \\ \text{ Replacing the values, we have: } \\ P=(480,000)/((((1+(0.05)/(12))^(21\cdot12)-1)/((0.05)/(12))))\text{ } \\ P=(480,000)/((((1+(0.05)/(12))^(252)-1)/((0.05)/(12))))\text{ (Multiplying 21 by 12)} \\ P=(480,000)/((((1+0.0042)^(252)-1)/(0.0042)))\text{ (Dividing)} \\ P=(480,000)/(((2.85-1)/(0.042)))\text{ (Adding and raising to the power of 452)} \\ P=(480,000)/((440.81))\text{ (Subtracting and dividing)} \\ P=1080.25\text{ (Dividing)} \\ \text{The answer is \$1080.25} \end{gathered}`