Question

• You decide to place $200 at the beginning of each month in an investment account earning interest at 4.33% annually (4.33% / 12 monthly). You plan on following this practice for five years (60 months). How much will you have accumulated in the account at the end of the five-year period?
• An investor invests $50 an account that returns 5% annually (5% / 12 per month). How much is the investor’s account worth at the end of the five-year period?

Gorman Corp. is attempting to build its cash reserves. Its CFO has determined that it can invest $35,000 at the beginning of each month in an account earning 6.42% annual interest (6.42% / 12 monthly). How long (in months) will Gorman need to follow this strategy to accumulate $3,000,000? – NOTE: This problem can be solved with the NPER() function or with GOAL SEEK.

Answer 1

Case 1 :	Future Value of an Annuity Due
	= C*[(1+i)^n-1]/i] * (1+i)
	Where,
	c= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $200[ (1+0.0036083333)^60 -1 /0.0036083333] * (1 +0.0036083333)
	= $200[ (1.0036083333)^60 -1 /0.0036083333] * 1.0036083333
	= $200[ (1.2412 -1 /0.0036083333] * 1.0036083333
	= $13,419.48
Case 2 :	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $50[ (1+0.05)^5 -1] /0.05
	= $50[ (1.05)^5 -1] /0.05
	= $50[ (1.2763 -1] /0.05]
	= $276.28
Case 3 :	Future Value of an Annuity Due
	c= Cash Flow	35000
	i= Interest Rate	0.00535
	n= Number Of Periods	n
	Future Value of an Annuity Due
	= C*[(1+i)^n-1]/i] * (1+i)
	Where,
	c= Cash Flow per period
	i = interest rate per period
	n=number of period
	3000000= $35000[ (1+0.00535)^n -1 /0.00535] * (1 +0.00535)
	3000000= $35000[ (1.00535)^n -1 /0.00535] * 1.00535
	n =70.43 months
	Number of months =70.43
	Number of years =5.87