A $4000 loan made at 11.75% is to b repaid in three equal payments, due 30, 90, and 150 days, respectively, after the date of the loan. Detemine the size of the payments.
Let the amount of each payment be represented by x.
P1=
______x__________=0.9904349x
1 + 0.01175(30/365)
P2=
_______x__________=0.9718432x
1 + 0.01175(90/365)
P3=
_______x__________=0.9539366x
1 + 0.01175(150/365)
$4000= P1 + P2 + P3
= 0.9904349x + 0.9718432x
+ 0.9539366x
=2.916215x
x= ___$4000___
2.916215
x= $1371.64
Therefore, each payment should be $1371.64.
My question is how do i get the answer in P1=0.9904349x, P2=0.9718432x, and
P3=0.9539366x. Just show me for one of them then i can understand how to do it for the rest. Thanks.
To directly answer your question, the values are:
x/(1 + 0.1175(30/365))
=x*(1/[1+0.1175(30/365)]
=x*(1/1.009657534246579)
=0.99043484159826x
You could not reproduce the answer because the expression was incorrect. The 0.1175 had been transcribed as 0.01175.
To determine the size of each payment (P1, P2, and P3), we need to calculate the present value of each payment. The present value represents the current value of a future payment, taking into account the time value of money.
Let's calculate the present value for P1:
P1 = x / (1 + r)^t
Where:
- x is the size of the payment (unknown)
- r is the interest rate per period, which is 11.75% or 0.1175 in decimal form
- t is the time in years until the payment is due, which is 30 days divided by 365 days (as the interest rate is given annually)
Substituting the values, we get:
P1 = x / (1 + 0.1175*(30/365))
Simplifying further:
P1 = x / (1 + 0.01175)
P1 = x / 1.01175
P1 = 0.9904349x
So, to determine the size of P1, you divide the payment amount (x) by 1.01175.
You can use a similar approach to calculate the present value for P2 and P3, but remember to adjust the time (t) accordingly for each payment.
I hope this explanation helps you understand how to get the answer for P1.