The current period is January 2015
A Principal wants to make 3 deposits in the bank:
Start of 2015,
Start of 2016,
Start of 2017,
And wants to give a $5000 scholorship for to the best student at the end of the following years:
$5000 end of 2018,
$5000 end of 2019,
$5000 end of 2020,
$5000 end of 2021,
$5000 end of 2022,
The interest rate is 6% p.a, everything is compounded yearly.
The Principal doesn't care about having money left over in the fund, he wants to use it exactly.
What are the three equal deposits in 2015,2016,2017 he needs to make so he can fund his scholorship program?
I am struggling with this problem any help?
At the end of the year 2022 the value of the deposits and the value of the withdrawals have to be equal.
The future value of the three deposits (x) is
$x\cdot 1.06^8+x\cdot 1.05^7+x\cdot 1.06^6=x\cdot 1.06^6\cdot(1.06^2+1.06+1)$
The future value of the withdrawals is
$\underbrace{5000\cdot 1.06^4}_{\text{FV of withd. 2018}}+\underbrace{5000\cdot 1.06^3}_{\text{FV of withd. 2019}}+\underbrace{5000\cdot 1.06^2}_{\text{FV of withd. 2020}}+\underbrace{5000\cdot 1.06^1}_{\text{FV of withd. 2021}}+\underbrace{5000\cdot 1.06^0}_{\text{FV of withd. 2022}}= 5000\cdot \frac{1.06^5-1}{0.06}$
Setting the future values equal:
$x\cdot 1.06^6\cdot(1.06^2+1.06+1)=5000\cdot \frac{1.06^5-1}{0.06}$
Now you can solve the equation for x.