If you deposit a lump sum of $5000 into a savings account at an interest rate of 7% per year, what will the value be after 10 years?

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Multiple Choice

If you deposit a lump sum of $5000 into a savings account at an interest rate of 7% per year, what will the value be after 10 years?

To determine the future value of a lump sum investment, we can use the formula for compound interest: \[ A = P (1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. In this case: - \( P = 5000 \) - \( r = 0.07 \) (7% converted to a decimal) - \( n = 10 \) Substituting these values into the formula gives: \[ A = 5000 (1 + 0.07)^{10} \] \[ A = 5000 (1.07)^{10} \] \[ A = 5000 \times 1.967151 \] (approximately, since \( (1.07)^{10} \approx 1.967151 \)) \[ A \approx 9835.76 \] This rounds to about $9,836, making it the future value of the initial investment after

To determine the future value of a lump sum investment, we can use the formula for compound interest:

[ A = P (1 + r)^n ]

Where:

  • ( A ) is the amount of money accumulated after n years, including interest.

  • ( P ) is the principal amount (the initial amount of money).

  • ( r ) is the annual interest rate (decimal).

  • ( n ) is the number of years the money is invested or borrowed.

In this case:

  • ( P = 5000 )

  • ( r = 0.07 ) (7% converted to a decimal)

  • ( n = 10 )

Substituting these values into the formula gives:

[ A = 5000 (1 + 0.07)^{10} ]

[ A = 5000 (1.07)^{10} ]

[ A = 5000 \times 1.967151 ] (approximately, since ( (1.07)^{10} \approx 1.967151 ))

[ A \approx 9835.76 ]

This rounds to about $9,836, making it the future value of the initial investment after

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