Question

You are planning to deposit in a savings account $25,000 three years from now, $35,000 in the fourth year, and $45,000 in six years. What is the current value of these savings at a discount rate of 7%?

a) $82,490.77
b) $77,094.18
c) $88.265.13
d) $34,330.28
e) $72,050.63

Answer 1

The current combined value of the future savings deposits of $25,000, $35,000, and $45,000 at a 7% discount rate is $77,094.18. This is determined by calculating the present value of each deposit and summing them up.

Step-by-step explanation:

To find the current value of the future savings, we need to calculate the present value (PV) of each deposit using the following Present Value formula: PV = FV / (1 + r)n, where FV is the future value of the deposit, r is the discount rate, and n is the number of years until the deposit is made.

First, we calculate the present value for the $25,000 deposit made three years from now: PV = $25,000 / (1 + 0.07)3 = $19,457.09.

Next, for the $35,000 deposit in the fourth year: PV = $35,000 / (1 + 0.07)4 = $25,690.63.

Finally, for the $45,000 deposit in six years: PV = $45,000 / (1 + 0.07)6 = $31,946.46.

To find the total current value, we add the present values of all three deposits: $19,457.09 + $25,690.63 + $31,946.46 = $77,094.18. Therefore, the direct answer is option b) $77,094.18.

This process is known as discounting, which reflects the principle that a dollar today is worth more than a dollar in the future due to the potential earning capacity.