Joe has withdrawn $1,238 from his account in year 3 and the value of his withdrawal has increased by 2% ever year after that till the end of year 9

Joe has withdrawn $1,238 from his account in year 3 and the value of his withdrawal has increased by 2% ever year after that till the end of year 9. How much did he need to deposit in a lump sum in year 0 in an account that earns 9% per year to be able to afford these withdrawals?

Please solve using formulas and not Excel.

Expert Solution

Present worth of geometric series = A*[1 - (1+g)^n/(1+i)^n]/(i-g)

Present worth of cash flow at EOY 2 = 1238*[1 - (1+0.02)^7/(1+0.09)^7]/(0.09-0.02)

= 1238*[1 - (1.02)^7/(1.09)^7]/(0.07)

= 1238*5.30899433

= 6572.53

Amount to be deposited at EOY 0 = 6572.53*(P/F,9%,2)

= 6572.53*0.841680

= 5531.97

Rahul Sunny answered 2 years ago

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