Question

you have your sights on buying. car costing 23,000 in two years time. Your bank account pats 5% interest compounded semi-annually. How much would you need to now in order to be able to buy your car in two years?

Answer 1

You would need to deposit approximately $20,829.48 now into an account that pays 5% interest compounded semi-annually to have $23,000 in two years to purchase a car.

Step-by-step explanation:

To determine how much you need to deposit now in order to buy a $23,000 car in two years with an account that pays 5% interest compounded semi-annually, you can use the formula for the present value (PV) of a future sum (FV):

PV = FV / (1 + r/n)^(nt)

Where:

• FV is the future value of the money, which is $23,000.
• r is the annual interest rate (0.05 for 5%).
• n is the number of times the interest is compounded per year (2 for semi-annually).
• t is the number of years the money is invested (2 years).

Using this information, the calculation is:

PV = $23,000 / (1 + 0.05/2)^(2*2)

PV = $23,000 / (1.025)^(4)

PV = $23,000 / 1.103812890625

PV ≈ $20,829.48

This means you would need to deposit approximately $20,829.48 now to have enough to buy the car in two years. Remember, the power of compound interest helps your investment grow over time, so starting to save early can significantly augment your savings as demonstrated by the example of investing $3,000 at a 7% real annual rate of return over 40 years.