Kayla plans to reduce her spending by $70 a month. Calculate the future value of this increase in savings over the next 10 years. (Assume an annual deposit to her savings account and an annual interest rate of 2 percent.)
Answer (2)
Kayla will save approximately $9,274.65 over the next 10 years by reducing her spending by $70 a month at an annual interest rate of 2%. This calculation uses the future value formula for a series of deposits. Factors such as the monthly interest rate and the total number of deposits are important in determining the future value.
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To calculate the future value of Kayla's increased savings over the next 10 years, we'll follow these steps:
Determine the Annual Savings :
Kayla plans to save $70 each month.
Therefore, her annual savings will be: 70 dollars/month × 12 months/year = 840 dollars/year
Use the Future Value Formula for Savings :
The formula for the future value of regular savings (or annuity) at the end of a period with a constant annual interest rate is given by: F V = P × r ( 1 + r ) n − 1 where:
F V is the future value of the savings.
P is the annual deposit (840 dollars in this case).
r is the annual interest rate (2% or 0.02 as a decimal).
n is the total number of years (10 years).
Plug the Values into the Formula : F V = 840 × 0.02 ( 1 + 0.02 ) 10 − 1
First, calculate ( 1 + 0.02 ) 10 : ( 1.02 ) 10 ≈ 1.21899
Subtract 1 from this result: 1.21899 − 1 = 0.21899
Divide this by the interest rate: 0.02 0.21899 = 10.9495
Finally, multiply by the annual savings: 840 × 10.9495 ≈ 9207.18
Conclusion :
The future value of Kayla's increased savings over the next 10 years at an annual interest rate of 2% will be approximately $9207.18. This is the total amount she will have saved at the end of the 10-year period, including the interest earned.
