Question

An investor wishes to accumulate 200 PLN. How many months must the investor pay 40 PLN at the beginning of each month if the interest rate is 12% per annum, compounding annually. Solve the problem of non-integer value of the term of annuities. Rework example with deposits at the end of each month.

Answer 1

1)	The first one is an annuity due.
	200 = 40*PVIF Annuity due(1,n)
	Solving for n
	5 = PVIF Annuity due(1,n)
	The value of n is to be found out by trial and error
	by finding out the interest factor for different
	interest rates.
	PVIF Annuity due at 9% for 4 months = 4.10101
	PVIF Annuity due at 9% for 5 months = 5.15202
	n lies between 4 and 5.
	The value of n by simple interpolation = 4+(5-4.10101)/(5.15202-4.10101) =	4.86
2)	The second one is an ordinary annuity.
	Using the same method.
	200 = 40*PVIFA(1,n)
	Solving for n
	5 = PVIFA(1,n)
	The value of n is to be found out by trial and error
	by finding out the interest factor for different
	interest rates.
	PVIF Annuity due at 9% for 4 months = 4.06040
	PVIF Annuity due at 9% for 5 months = 5.10101
	n lies between 4 and 5.
	The value of n by simple interpolation = 4+(5-4.06040)/(5.10101-4.06040) =	4.90