You deposit $100 at the end of each quarter in a sinking fund earning 4% compounded quarterly. How many quarterly deposits must you make in order to reach your goal of saving $10,000? Round your answer off to the nearest whole number.

Question

You deposit $100 at the end of each quarter in a sinking fund earning 4% compounded quarterly. How many quarterly deposits must you make in order to reach your goal of saving $10,000? Round your answer off to the nearest whole number.

Answer 1

i=4% p.a. compounded quarterly

= 1% per period

Let
R=(1+i),
n= number of quarters/periods

Future value
FV=100(1+R+R²+R³....+R^(n-1) )
=100(R^n-1)/(R-1)
=100(R^n-1)/i

For FV=10000
we have
10000=100(R^n-1)/i
R^n=(10000/100)*i-1
=2
n=log(2)/log(1.01)=69.66
It will take 70 quarters to reach $10000.

Check:
FV=100(1.01^70-1)/0.01=$10067 :)