Question

# You have $50,000 in savings for retirement in an investment earning 9% annually. You aspire to have$1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth. Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.

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## Answer to a math question You have $50,000 in savings for retirement in an investment earning 9% annually. You aspire to have$1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth. Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.

Eliseo
4.6
To calculate the number of years needed to reach the savings goal, we can use the future value formula for compound interest:

FV = PV \times $1 + r$^n

where:
- FV is the future value you want to achieve $\$1,000,000$, - PV is the present value $initial savings,$50,000$,
- r is the annual interest rate $9% or 0.09$, and
- n is the number of years.

Plugging in the given values, we have:

\50,000 \times $1 + 0.09$^n

20 = $1.09$^n

To solve for n , we will use logarithms:

n = \frac{{\ln$20$}}{{\ln$1.09$}}

n\approx34.76

Therefore, it will take approximately 34.76 years to reach \$1,000,000 in savings, rounded to the nearest hundredth.

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