Joe is getting ready to buy a car. He has $20,000 in investments earning 4.9% annually. The car also costs $20,000. If he doesn’t pay cash for the car, Joe can get a loan at 2.9% interest for 5 years. The loan is structured so that Joe pays one balloon payment at the end of 5 years. The balloon payment includes the principal plus all interest accrued over 5 years. If Joe takes the loan will he have enough money available from his investments to make the balloon payment? How much will he be short/have to spare?
well, you can use the Excel to solve this question. first, you can calculate two FV. then using the result of fv 25404.31-23073.15=2331.16 so, he can pay the balloon payment and will spare $2331.16
To determine if Joe will have enough money available from his investments to make the balloon payment, we need to calculate the amount of interest earned by his investments over 5 years.
Step 1: Calculate the interest earned annually:
Interest Earned = Principal * Interest Rate
Interest Earned = $20,000 * 4.9% = $980 per year
Step 2: Calculate the total interest earned over 5 years:
Total Interest Earned = Interest Earned * Number of Years
Total Interest Earned = $980 * 5 = $4,900
Step 3: Calculate the total amount available from investments:
Total Amount Available = Principal + Total Interest Earned
Total Amount Available = $20,000 + $4,900 = $24,900
Next, let's calculate the balloon payment amount for the car loan:
Step 4: Calculate the interest accrued over 5 years on the car loan:
Interest Accrued = Principal * Interest Rate * Number of Years
Interest Accrued = $20,000 * 2.9% * 5 = $2,900
Step 5: Calculate the balloon payment amount:
Balloon Payment = Principal + Interest Accrued
Balloon Payment = $20,000 + $2,900 = $22,900
Now we can determine if Joe will have enough money available from his investments to make the balloon payment:
Step 6: Calculate the difference between the total amount available and the balloon payment:
Difference = Total Amount Available - Balloon Payment
Difference = $24,900 - $22,900 = $2,000
Based on the calculations, Joe will have $2,000 to spare if he takes the car loan.
To determine whether Joe will have enough money available from his investments to make the balloon payment, we need to calculate the future value of his investments after 5 years.
First, let's calculate the future value of his investments after 5 years, earning 4.9% annually. The future value can be calculated using the formula:
FV = PV * (1 + r)^n
Where:
FV = Future Value (amount of money after 5 years)
PV = Present Value (initial investment)
r = Interest rate per period
n = Number of periods
Here, PV = $20,000 (Joe's current investment), r = 4.9% = 0.049 (4.9% expressed as a decimal), and n = 5 years.
Plugging these values into the formula, we get:
FV = $20,000 * (1 + 0.049)^5
Calculating this, the future value of Joe's investments after 5 years is approximately $24,241.
Now, let's calculate the balloon payment amount, which includes the principal and all interest accrued over 5 years.
To calculate the balloon payment, we can use the formula for the future value of a loan:
Balloon Payment = Principal * (1 + r)^n
Here, the principal is $20,000 (the cost of the car), r = 2.9% = 0.029, and n = 5 years.
Plugging these values into the formula, we get:
Balloon Payment = $20,000 * (1 + 0.029)^5
Calculating this, the balloon payment amount is approximately $22,724.
Now, let's compare the future value of Joe's investments ($24,241) with the balloon payment amount ($22,724).
Joe will be left with $24,241 - $22,724 = $1,517 after making the balloon payment.
Therefore, Joe will have $1,517 to spare after making the balloon payment.
I = PRT
I = 20,000 * 0.049 * 5
I = $4,900
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I = 20,000 * 0.029 * 5
I = ?