Question

Today, you invest a lump sum amount in an equity fund that provides an 12% annual return. you would like to have $12,300 in 6 years to help with a down payment for a home. how much do you need to deposit today to reach your $12,300 goal?

Answer 1

To reach a goal of $12,300 in 6 years with a 12% annual return, you should invest approximately $6,109.63 today. This is calculated using the present value formula.

Step-by-step explanation:

To calculate the amount you need to deposit today to reach your future goal of $12,300 with an annual return rate of 12%, you can use the formula for the present value of a future sum:

PV = FV / (1 + r)^n

Where:

• PV is the present value,
• FV is the future value which is $12,300,
• r is the annual interest rate (0.12 in this case),
• n is the number of years (6 in this case).

Plugging in the values:

PV = $12,300 / (1 + 0.12)^6

Calculating the denominator first:

(1 + 0.12)^6 ≈ 2.0122

Dividing the future value by this number gives us:

PV = $12,300 / 2.0122 ≈ $6,109.63

Therefore, you need to invest approximately $6,109.63 today to have $12,300 in 6 years, assuming a 12% annual return.