Rebecka borrowed $3500, 5000, 3500,& 4500 from her dad on September 1 of each of four successive years for college expenses. Rebecka and her dad agreed to a loan at the rate of 8.75% compounded quarterly. If it is now 2 years from the last day that she borrowed money, how much woruld Rebecka owe?
The correct answer is $22,352.25
but i got the wrong answer, and the formula for this question is
FV=PV(1+i/4)^4*n
i=j/m
=8.75%/4
=0.021875
n= mt
=(4)(2)
= 8
FV=3500(1+.021875/4)^4*8
=4167.37
FV=5000(1+.021875/4)^4*8
=5953.40
FV=3500(1+.021875/4)^4*8
=4167.37
FV=4500(1+.021875/4)^4*8
=5358.05
then i sum all up and i get $19,646.19 and the answer should be $22,352.25
!!!
Assuming you placed the loans in the correct order,
the first $3500 earns interest for 20 periods (5 years)
the $500 earns interest for 16 periods (4 years)
the $3500 for 12 periods (3 years)
and the last $4500 for 8 periods (2 years)
You would need
4500(1.021875)^8 + 3500(1.021875)^12 + 5000(1.021875)^16 + 3500(1.021875)^20
= 20352.28
which is their answer.
I carried all my digits of my 10 digit calculator.
thnx Reiny!!! :-D
To find the total amount owed by Rebecka after 2 years, you need to add up the individual future values of each loan she took from her dad. Let's go through the calculations step by step:
1) Calculate the future value of the first loan of $3500:
FV1 = 3500 * (1 + 0.0875/4)^(4*2) = 3500 * (1.021875)^8 = 3500 * 1.1839746 = $4,137.91
2) Calculate the future value of the second loan of $5000:
FV2 = 5000 * (1 + 0.0875/4)^(4*2) = 5000 * (1.021875)^8 = 5000 * 1.1839746 = $5,919.87
3) Calculate the future value of the third loan of $3500:
FV3 = 3500 * (1 + 0.0875/4)^(4*2) = 3500 * (1.021875)^8 = 3500 * 1.1839746 = $4,137.91
4) Calculate the future value of the fourth loan of $4500:
FV4 = 4500 * (1 + 0.0875/4)^(4*2) = 4500 * (1.021875)^8 = 4500 * 1.1839746 = $5,332.56
5) Sum up the individual future values:
Total amount owed = FV1 + FV2 + FV3 + FV4
Total amount owed = $4,137.91 + $5,919.87 + $4,137.91 + $5,332.56 = $19,528.25
Based on these calculations, it seems you made a mistake in one of your calculations. The correct total amount owed by Rebecka after 2 years is $19,528.25, not $22,352.25.
It seems like you're on the right track with the formula you're using. The formula you're using, FV = PV(1 + i/m)^(m*t), is the correct formula for compound interest where PV represents the principal amount, i represents the interest rate, m represents the number of compounding periods per year, and t represents the number of years.
Double-check your calculations and make sure you're accurately calculating the future value for each individual loan amount.
Here's how you can solve the problem step-by-step:
1. For the first loan of $3500, the future value (FV) would be:
FV = 3500 * (1 + 0.0875/4)^(4*2) = $4,167.37
2. For the second loan of $5000, the future value would be:
FV = 5000 * (1 + 0.0875/4)^(4*2) = $5,953.40
3. For the third loan of $3500, the future value would be:
FV = 3500 * (1 + 0.0875/4)^(4*2) = $4,167.37
4. For the fourth loan of $4500, the future value would be:
FV = 4500 * (1 + 0.0875/4)^(4*2) = $5,358.05
Now, add up all the future values:
$4,167.37 + $5,953.40 + $4,167.37 + $5,358.05 = $19,646.19
It seems like you made a mistake in your calculations or possibly made an error in rounding. Check your calculations again, and make sure you're using the correct values for each loan. If you still can't find the mistake, please double-check the problem statement to ensure all the information is correct.