David’s friend, Keanu, has hired a financial planner for advice on retirement. Considering Keanu’s current expenses and expected future lifestyle changes, the financial planner has stated that once Keanu crosses a threshold of $7,796,223 in savings, he will have enough money for retirement. Keanu has nothing saved for his retirement yet, so he plans to start depositing $70,000 in a retirement fund at a fixed rate of 9.00% at the end of each year. It will take ___ years for Keanu to reach his retirement goal.

Keanu has decided to save a fixed amount of 70,000 for a given period. We would need to calculate the number of years to achieve 7,796,223 using the FVIFA formula (Future value interest for an annuity)

Fixed payment× FVIFA=Future value

FVIFA = [tex]\frac{(1+r)^{n} - 1}{r}[/tex]

where r is the periodic rate (9%)

and n is the number of periods

therefore; 70000×[tex]\frac{(1+0.09)^{n} - 1}{0.09}[/tex]=7796223

[tex]{(1+0.09)^{n} }[/tex]=(7796223×0.09)/70000

n=27.85

However, since Keanu will not invest until the end of the first year, he will spend 28.85 years to achieve his goal