You decide you want to buy a house in 4 years and need to have a down payment of $80,000. A high yield money market account has an annual interest rate of 6%. Which calculation would you use to determine if a monthly deposit of $500 would be enough to reach your goal?

Question

1)FV=500[(1+0.005)^48 -1]/[0.005]
2)FV=500[(1+0.06)^48 -1]/[0.06]
3)FV=500[(1-0.005)^48 -1]/[0.005]
4)FV=500[(1+0.005)^4 -1]/[0.005]

Answer 1

To determine whether a monthly deposit of $500 will be enough to reach a goal of $80,000 in 4 years in a high yield money market account with an annual interest rate of 6%, we can use the formula for the future value of a series of cash flows (deposits):

The future value formula for a series of regular deposits (ordinary annuity) is given by:

\[ FV = P \times \left[ \frac{(1 + r)^n - 1}{r} \right] \]

Where:

• \( FV \) = future value of the investment/loan including interest
• \( P \) = deposit amount (monthly deposit)
• \( r \) = interest rate per period (monthly interest rate)
• \( n \) = number of total deposits (number of periods)

In this case:

• The monthly deposit \( P = 500 \).
• The annual interest rate is 6%, so the monthly interest rate \( r = \frac{0.06}{12} = 0.005 \).
• The total number of deposits over 4 years (48 months) is \( n = 4 \times 12 = 48 \).

Inserting these values into the future value formula, we get:

\[ FV = 500 \times \left[ \frac{(1 + 0.005)^{48} - 1}{0.005} \right] \]

Thus, the correct calculation to determine if a monthly deposit of $500 would be enough to reach your goal of $80,000 is:

1) FV = 500[(1 + 0.005)^{48} - 1]/[0.005]