Question

You decide to put $2,000 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds? 121. 862 years 12. 1862 years 10. 155 years 1. 0155 years.

Answer 1

The correct statement is that it will take 10.155 years to accumulate $3000 on an initial investment of $2000 for the down payment of the car. Future value will be calculated for this purpose. The correct option is C.

The computation will be done by calculating the future value by the way of applying the given information to the formula of calculation of future value of the deposit. We are using an optional method for this calculation.

Calculation of future value

• The future value of an annuity deposit can be calculated by using the formula given below and applying the values given to us in the information regarding the deposit,

• $\rm Future\ Value\ of\ Annuity= 2000(1+ \dfrac{0.04}{12})^1^2 ^x^1^0^.^1^5^5\\\\\rm Future\ Value\ of\ Annuity=\ 2999.58$

• So, it can be concluded that it will take about 10 years for the amount to become $3000 at the rate of 4 percent.

Hence, the correct option using the substitution method of future value  is C that it will take 10.155 years for the amount to become $3000 over an annual interest rate of 4 percent compounded monthly.

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