Question

You decide to put $5,000 in a savings account to save for a $6,000 downpayment on a new car. If the account has an interest rate of 7% per year and is compounded monthly, how long does it take until you have $6,000 without depositing any additional funds? 313. 464 years 31. 346 years 26. 122 years 2. 612 years.

Answer 1

The correct relevant amount of time taken by investment of $5000 to become $6000 will be 2.612 years. So the correct option that matches the quoted statement is D.

Compound Interest formula will be applied to calculate such investment to achieve the desired amount for the purpose of payment of down-payment of the car.

• Compound Interest is basically referred to as the interest over the accrued interest achieved over such time frame over the top of interest received on principal amount of investment.

• The formula of compound interest compounded monthly is as given below,

• $\rm Compound\ Interest= P(1+\ \dfrac {r}{n})^n^t$

• Using the formula we can say that we require an interest of $1000 so that the amount becomes $6000. We can use the formula and put the values as under.

• $\ 1000= \ 5000(1+ \dfrac{0.07}{12})^1^2^t$

• This can also be written as,

• $t = \dfrac {6,000.00/5,000.0}{12\×\ (1 + 0.07/12)}$

• Calculating further,

• $t = \dfrac {6,000.00/5,000.00} { 12\ \rm x\ (1 + 0.005833333)}$

• Which comes down to,

• $t= 2.612\ \rm Years$

• So we can say that it takes 2.612 years to make such investment into $6000 at the interest rate of 7% which is compounded on a monthly basis.

Hence, the correct option is C is that it will take 2.612 years to get returns as $6000 over such investment at the interest rate of 7 percent per year.

To know more about compound interest, click the link below.

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