Question 1093018: Jim put $2000 a year into an investment every year for 15 years. The investment paid 6% interest per annum. At the end of the fifteen years he moved the accumulated amount including the interest earned and invested it in a GIC that paid 8% compounded quarterly. He left the investment for the next 10 years. Approximately how much money did he have at the end of the twenty-five years?
Answer by greenestamps(13203)   (Show Source):
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The formula for the value V of an investment of A made regularly for n years at an interest rate of r is
Find the value V for your problem where the regular deposit A is 2000, the interest rate is 6% (that is, .06), and the number of years n is 15.
After the regular contributions stop and the money just sits there gaining interest, the compound interest formula for the final value A is the beginning principal P, multiplied by the periodic growth factor (1 plus r, where r is the periodic interest rate; i.e., the annual interest rate divided by the number of periods per year) n times, where n is the number of compounding periods:
In your problem, the beginning principle P for these last 10 years is the ending value after the first 15 years, as found previously; the periodic interest rate is one-quarter of the 8% annual interest rate (again, as a decimal), since compounding is quarterly; and the number of compounding periods n is 40 since the compounding is 4 times a year for 10 years.
As a check for your calculations, I found the value after 15 years to be $46,551.94 and the final value after 25 years to be $102,788.53.
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