Question

4) If a person deposits $2000 in to an account paying 6% compounded annually one year from now and then increases his deposits by 100$ each year for the next eight years, determine the amount of money that will be in the account at the end of eight years.

5) What is the equivalent present amount of a fifteen year period series of decreasing amounts if the interest rate is 12% compounded annually the first year amount is $35000 and the rate of decrease is $1050 per year.

Answer 1

Answer to Question 4:

Initial deposit = $2,000
Annual deposit = $100
Annual interest rate = 6.00%
Period = 8 years

Accumulated sum = $2,000*1.06^8 + $100*1.06^7 + $100*1.06^6 + … + $100*1.06 + $100
Accumulated sum = $2,000*1.06^8 + $100 * (1.06^8 - 1) / 0.06
Accumulated sum = $2,000 * 1.593848 + $100 * 9.897468
Accumulated sum = $4,177.44

So, balance of account at the end of eight years is $4,177.44