Original practice · fully worked
Original variant: loan principal from two principal portions
An eight-payment level loan has principal portions 900 in payment 2 and 1,093.50 in payment 6. Principal portions grow geometrically with the loan rate. Calculate the original loan principal.
- A
7,200.00 - B
7,534.18 - C
7,943.76 - D
8,182.60 - E
8,548.22
Answer and calculation
The rate is 4.99%, first principal is 857.23, and the geometric principal sum is 8182.60. The original loan is 8,182.60, which is choice D.
Setup
Setup
Use the four-payment gap between the two principal portions to recover the loan rate.
900(1+i)4=1093.50⟹i=0.04989065 Model
Model
Back up one period to obtain principal in payment 1, then sum all eight principal portions because their total equals original principal.
P1=900/(1+i)=857.232129 Compute
Compute
The rate is 4.99%, first principal is 857.23, and the geometric principal sum is 8182.60.
L=k=1∑8P1(1+i)k−1=8182.602194 Answer
Answer
The original loan is 8,182.60, which is choice D.
L=8182.60(D) 