Question

Richie Rich is a wealthy man that have decided to create a fund to give scholarships to college students. His intention is to start providing scholarships for a quantity of $200,000 every year starting on January 1^st, 2025, quantity that will be given every year during the rest of the time. For this, on January 1^st of 2010, Richie deposited a quantity “X” of money. Every subsequent year until January 1^st, 2019 he will deposit $15,000 more than the previous year. The account will bear 10% on annual interest, rate that is guarantee during the rest of the time.

a. Determine the quantity of Richie Rich’s deposit on January 1^st of 2010.

b. Determine the quantity of Richie Rich’s last deposit on January 1^st of 2019.

Answer 1

He invests X on 1st jan 2010 then increases amount by $15000 till 2019 hence total amount till 2019 is

[X*(1.1)^9+(X+15000)*(1.1)^8+(X+30000)*(1.1)^7+(X+45000)(1.1)^6+...+(X+135000)(1.1)^1](1.1)^6=200000/0.1=2,000,000

By using solver we can find the X needed to be 69,608.88

and Richies Last Deposit is 69608.88+135000=$204,608.88

And on 1st Jan 2010 he deposited $69608.88

I hope these steps will clarify your doubts..If there is any mistake then it wouold be in power of (1.1) otherwise idea i used to solve this problem is efficient.

Best of Luck Student