John plans to retire in 30 years and sets up a sinking fund to accrue $1,000,000. The annual interest rate is 5% and interest is compounded quarterly.

Question

Sinking Fund - have no idea what formula to use and how to determine answers to A and B:

 

A)  If she makes equal payments at the end of each quarter, find the amount of each payment that is necessary to achieve her goal.  B) How much interest will she earn?

Answer 1

The formula for sinking fund:

 

A = R[(1+r)ⁿ-1]/i, where A = final amount,  r = interest rate, n = number of periods, R = monthly contributions.

 

1000000 = R[(1 + 0.05)¹²⁰ -1] / 0.05       n = 4 quarters times 30 years.

1000000 = R[(1.05)¹²⁰ - 1] / 0.05

50000 ≈ R[34.89 - 1]

50000 ≈ R[33.89] 

1475.36 ≈ R

 

John must make a monthly payment of $1,475.36.

 

The interest earn is the final amount, $1,000,000 - the payments, 120(1475.36).

1000000 - 177043.34 = 822956.67

 

The earned interest is $822,956.67