Question

A company has a $170,000 note due in 3 years. How much should be deposited at the end of each quarter in a sinking fund to pay off the note in 3 years if the interest rate is 11% compounded quarterly?

Answer 1

Assume amount deposited =x

so interest rate = 11% compounded quarterly so per quarter interest rate is 11%/4=2.750%

future value = present value*(1+r)^n

no of periods = no of years*4 quarters per year=3*4=12 periods

170000= investment amount*((1+2.750)^12+(1+2.750)^11+(1+2.750)^10+(1+2.750)^9+(1+2.750)^8+(1+2.750)^7+(1+2.750)^6+(1+2.750)^5+(1+2.750)^4+(1+2.750)^3+(1+2.750)^2+(1+2.750)^1)

170000=investment amount *(14.3769)

so invested amount =170000/14.3769

=11824.5

So investment amount each quarters=11824.5