You want to withdraw $39,944 from your account that the end of one year and $24,608 at the end of the second year. How much should you deposit in your account today so that you can make these withdrawals? Your account pays 15 percent p.a.
Answer: $53,341.10
Can someone provide me the actual steps to solve this problem? Thank you!
To solve this problem, you need to use the concept of present value and future value of money. The idea is that the value of money today is different from its value in the future due to factors such as interest rates and inflation.
Here are the steps to find out how much you should deposit today:
Step 1: Calculate the future value of the first withdrawal (at the end of one year):
FV1 = future value
PV1 = present value (unknown)
r = interest rate = 15% = 0.15
n = number of periods (years) = 1
FV1 = PV1 * (1 + r)^n
$39,944 = PV1 * (1 + 0.15)^1
$39,944 = PV1 * 1.15
Step 2: Calculate the future value of the second withdrawal (at the end of the second year):
FV2 = future value
PV2 = present value (unknown)
r = interest rate = 15% = 0.15
n = number of periods (years) = 2
FV2 = PV2 * (1 + r)^n
$24,608 = PV2 * (1 + 0.15)^2
$24,608 = PV2 * 1.3225
Step 3: Set up an equation using the two future values and the present values:
PV1 + PV2 = total deposit (unknown)
Step 4: Substitute the expressions for PV1 and PV2 from Steps 1 and 2 into the equation:
$39,944/1.15 + $24,608/1.3225 = total deposit
Step 5: Calculate the total deposit:
$34,720 + $18,611.98 ≈ total deposit
Total deposit ≈ $53,331.98
Therefore, you should deposit approximately $53,331.98 into your account today in order to make the desired withdrawals. However, since the answer provided is rounded to the nearest penny, the final answer will be $53,341.10.