Question

. How much would you have to deposit today if you wanted to have $66,000 in four years? Annual interest rate is 9%. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your answer to the nearest whole dollar.) b. Assume that you are saving up for a trip around the world when you graduate in two years. If you can earn 8% on your investments, how much would you have to deposit today to have $18,500 when you graduate? (Round your answer to 2 decimal places.) c-1. Calculate the future value of an investment of $787 for ten years earning an interest of 9%. (Round your answer to 2 decimal places.)

Answer 1

The present value formula is used to determine how much to deposit today to accumulate a specific amount in the future at a given interest rate. In these scenarios, one must calculate the present value for $66,000 in 4 years at 9% interest, $18,500 in 2 years at 8% interest, and the future value of $787 over 10 years at 9% interest.

Step-by-step explanation:

To calculate how much you would have to deposit today to have $66,000 in four years at an annual interest rate of 9%, you can use the present value formula which is PV = FV / (1 + i)^n. Here, FV is the future value of $66,000, i is the interest rate (0.09 in decimal form), and n is the number of years (4 years). Plugging in the values, we get PV = $66,000 / (1 + 0.09)^4, which, upon calculation, gives us the amount that needs to be deposited today.

Similarly, to have $18,500 in two years at an interest rate of 8%, use the formula again with FV as $18,500, i as 0.08, and n as 2. This gives us PV = $18,500 / (1 + 0.08)^2.

Finally, to calculate the future value of an investment of $787 for ten years at an interest rate of 9%, we use the future value formula FV = PV (1 + i)^n. This gives us FV = $787 * (1 + 0.09)^10. Calculation of these values will give us the respective amounts rounded to the nearest whole dollar or two decimal places as required.

Answer 2

a. To have $66,000 in four years with an annual interest rate of 9%, the present value is:

PV = $66,000 x discount factor

= $66,000 x (1.09)^4

= $66,000 x 0.708

= $46,728

b. To have $18,500 in two years with an interest rate of 8% yearly, the present value is:

PV = $18,500 x discount factor

= $18,500 x (1.08)^2

= $18,500 x 0.857

= $15,854.50

c. The future value of an investment of $787 for ten years earning an interest of 9% is:

FV = $787 x FV factor

= $787 x (1.09)^10

= $787 x 2.367

= $1,862.83

Step-by-step explanation:

The present values for options A and B are calculated by discounting the future values with their discount factors. The present values show the amounts that need to be invested today at prevailing interest rates to yield the future values after the indicated periods of time.

The future value for option C is calculated by multiplying the present value of the investment with its future value factor. These present and future values show that there is a time value of money. This concept means that money received today is not equal in value to the same amount received some time later. Based on this difference, interest rates are charged to equate the values of money received today and money received in a year's time. The interest rates also consider the inflation rate and must always be above the inflation rate in order to retain future value.