Question

Theobald owns an investment that began with his 30,000 up front deposit and 120 monthly payments. The investment is growing at an annual rate of 11.73%, Theovald wants to know how much his investment grew in value from year 30 to 33. what was Theovalds total investment growth in those three years?

Answer 1

	Step 1.
	The upfront payment is 30000
	Interest rate =11.73%
a	Maturity value after 29 year =30000*(1+11.73%)^29 =	748,247.75
	Step 2.
	There are 12 monthly payments of 30,000
	Interest rate per month=11.73%/12=0.9775% per month
	Formula for future value of Ordinary Annuity :
	FV= A [ {(1+k)n-1}/k]
	FV = Future annuity value
	A = monthly   investment=30,000
	K=interest rate=0.9775% per month
	N=periods=120 months
	FV after 10 years=30000*[1.009775^120-1]/0.9775%=	6,792,791.84
b	Fund Value after another 19 year =6792791.84*(1+11.73%)^19=	55,882,327.05
	Step 3.
c	So Total Value of Investment at the start of 30th Year=a+b=	56,630,574.80
d	Value of Investment 33 year end (in another 3 years)=56630574.80*(1+11.73%)^3=	78,987,863.33
e	Investment growth in year 30 to 33=d-c=	22,357,288.53