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How much would you need to deposit in an account now in order to have $3000 in the account in 10 years? Assume the interest rate is 6% compounded monthly.

A. $1,801.89
B. $2,830.19
C. $1,415.09
D. $2,250.00

1 Answer

3 votes

Final answer:

To have $3000 in 10 years at a 6% interest rate compounded monthly, you would need to deposit approximately $1650.73 now. The formula for present value was used to calculate this, and the answer doesn't match the provided options, suggesting there could be a mistake in the calculations or the choices given.

Step-by-step explanation:

To find out how much you would need to deposit now in order to have $3000 in an account in 10 years with an interest rate of 6% compounded monthly, you can use the formula for the present value of a future amount under compound interest:

P = A / (1 + r/n)(nt)

Where:

  • P is the present value, or the amount you need to deposit now
  • A is the future amount, which is $3000
  • r is the annual interest rate (decimal), so 0.06 for 6%
  • n is the number of times the interest is compounded per year, which is 12 for monthly
  • t is the number of years the money is invested, which is 10

Plugging in the values:

P = 3000 / (1 + 0.06/12)(12*10)

Calculating the exponent first:

P = 3000 / (1 + 0.005)120

Next, calculate the value inside the parentheses:

P = 3000 / (1.005)120

P = 3000 / (1.81939)

Finally, divide $3000 by 1.81939:

P = $1650.73

So, the amount you would need to deposit now is approximately $1650.73. However, this number isn't in the provided options, meaning there might have been a mistake in the calculation or provided options. It's essential to recheck the calculation or the actual question's conditions if the mismatch persists.

User Serberuss
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