Question

You want to retire in 46 years with $10,000,000. You plan to start saving next year and then growing each retirement contribution by 1% per year. You are confident that you can compound your savings at 9% per year. How much must your first payment be?

(future value of growing annuity problem) - please show work

Answer #1

Using goal seek

first payment is 15656.72

Future value of Growing annuity = |
P/(r - g) × [ (1+r)^{n} - (1+g)^{n}] |
|||

P= | Periodic payment | 15,656.72 | ||

g= | Growth rate | 1% | ||

r= | Rate of interest per period: | |||

Annual rate of interest | 9.00000% | |||

Frequency of payment | once in every 12 months | |||

Payments per year | 12/ 12= | 1 | ||

Interest rate per period | 0.09/1= | 9.00000% | ||

n= | number of payments: | |||

Number of years | 46 | |||

Payments per year | 1 | |||

number of payments | 46 | |||

Future value of annuity= | 15656.72/(0.09 - 0.01) × [ (1 + 0.09 )^46 - (1+ 0.01)^46 ] | |||

Future value of annuity= | 10,000,002.45 |

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