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
FV=3500(1+.021875/4)^4*8 i=j/m
=4167.37 =8.75%/4
=0.021875
FV=5000(1+.021875/4)^4*8
=553.40 n= mt
=(4)(2)
FV=3500(1+.021875/4)^4*8 = 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
oh the answer is posted got mixed up!!! :-S
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
!!!
To calculate how much Rebecka would owe after 2 years from the last day she borrowed money, you can use the formula for compound interest:
FV = PV(1 + i/n)^(n*t)
Where:
FV = Future Value (amount owed after a certain period)
PV = Present Value (initial amount borrowed)
i = interest rate per period (convert the annual rate to quarterly by dividing it by 4)
n = number of compounding periods per year
t = number of years
In this case, Rebecka borrowed $3500, $5000, $3500, and $4500 in four successive years. Since it is 2 years from the last day she borrowed money, t = 2.
Now we can calculate the future value for each loan and sum them up to get the total amount owed.
For the first loan of $3500:
PV1 = $3500
i = 8.75% (annual interest rate) / 4 = 2.1875% (quarterly interest rate)
n = 4 (compounded quarterly)
t = 2
FV1 = $3500(1 + 0.021875/4)^(4*2)
= $3500(1.00546875)^(8)
= $3500 * 1.04402445
= $3654.087575
For the second loan of $5000:
PV2 = $5000
i = 8.75% (annual interest rate) / 4 = 2.1875% (quarterly interest rate)
n = 4 (compounded quarterly)
t = 2
FV2 = $5000(1 + 0.021875/4)^(4*2)
= $5000(1.00546875)^(8)
= $5000 * 1.04402445
= $5220.12225
For the third loan of $3500:
PV3 = $3500
i = 8.75% (annual interest rate) / 4 = 2.1875% (quarterly interest rate)
n = 4 (compounded quarterly)
t = 2
FV3 = $3500(1 + 0.021875/4)^(4*2)
= $3500(1.00546875)^(8)
= $3500 * 1.04402445
= $3654.087575
For the fourth loan of $4500:
PV4 = $4500
i = 8.75% (annual interest rate) / 4 = 2.1875% (quarterly interest rate)
n = 4 (compounded quarterly)
t = 2
FV4 = $4500(1 + 0.021875/4)^(4*2)
= $4500(1.00546875)^(8)
= $4500 * 1.04402445
= $4715.6499375
Now sum up all the future values:
Total amount owed = FV1 + FV2 + FV3 + FV4
= $3654.087575 + $5220.12225 + $3654.087575 + $4715.6499375
= $17243.9473375
Therefore, the correct answer is $17,243.95, not $22,352.25.