Question

You recently inherited $10,000 and deposited the money today in an investment account paying 8% compounded annually. Inheriting this money has motivated you to plan for the future and you have decided that you would like to have $250,000 in the bank 15 years from today. To achieve this goal, in addition to the money you have already deposited in the investment account, you plan to deposit an equal amount of money in the account each year for the next ten years with your first deposit being made one year from now (there will be ten total deposits). How much must you deposit each year to achieve this goal?

Answer 1

Inheritance	10000
Interest rate	8%
Period in years	15
Amount=	Investment * (1+Interest)^Time
Amount=	10000*(1+8%)^15
Amount=	$ 31,721.69
Required corpus at T15	$250,000.00
Remaining corpus to be accumulated from annuity=	250000-31721.69
Remaining corpus to be accumulated from annuity=	$218,278.31
Value of this remaining amount at T10=	218278.31/(1+8%)^5
Value of this remaining amount at T10=	$148,556.55
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	$148,556.55
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	10
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
148556.55=	PMT x ((((1 + 8%) ^ 10) - 1) / 8%)
Annual deposit=	148556.66/ ((((1 + 8%) ^ 10) - 1) / 8%)
Annual deposit=	$ 10,254.78