A geometrically increasing series of 20 end of year payments is deposited to fun

Question

A geometrically increasing series of 20 end of year payments is deposited to fund an account. The first payment is $20,000, the geometric factor is 4%. The account is used for retirement purposes and will produce 30 consecutive annual payments of $60,000, starting at the end of year 16. Calculate the interest rate necessary to create this cash flow.

If the $60,000 payments start at the same point, but go on forever, what is the interest rate?

PLEASE SHOW ALL WORK AND EQUATIONS USED TO GET FINAL ANSWERS

Explanation / Answer

geometrically increasing series of 20 end of year payments first payment is $20,000 geometric factor is 4% Meaning each payment increase by 4% each time. 1st...$20,000 20,800 21,632 22,497.28 23,397.17 24,333.05 25,306.38 26,318.63 27,371.38 28,466.23 29,604.88 30,789.08 32,020.64 33,301.47 34,633.52 16th....$36,018.87 Add them all up, and compare it to $60,000 * 30 payments=$1,800,000 This is a very long question but I hope this helped, best of luck.

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