RatedrillGrowing annuity
A time value of money problem from Ratedrill. Solve it with one answer box, with fresh numbers on every attempt and the formula, calculator keystrokes and Excel version in the worked answer, and it is checked the moment you submit.
The task
A pension pays $13,000 at the end of the first year, and each later payment is 1% larger than the one before. There are 24 payments in all. At a discount rate of 7%, what is the pension worth today?
What this problem teaches
The formula: PV = C1 / (r - g) × (1 - ((1 + g) / (1 + r))^n). Shortcut: use the growth-adjusted rate I/Y = ((1 + r) / (1 + g) - 1) × 100 and PMT = C1 / (1 + g). Set P/Y = C/Y = 1, so I/Y is the rate per period. Cash you pay out is negative and cash you receive is positive.
A hint if you get stuck
PV = C1 / (r - g) × (1 - ((1 + g) / (1 + r))^n).
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