Question

Bryna wants to buy a car that is available at two dealerships. The price of the car is the same at both dealerships. Best Buggies would let her make quarterly payments of $2,240 for 5 years at a quarterly interest rate of 3.72 percent. Her first payment to Best Buggies would be due in 3 months. If California Cars would let her make equal monthly payments of $935 for 4 years and if her first payment to California Cars would be today, then what is the monthly interest rate that Bryna would be charged by California Cars? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I
2
3		The value of the car can be calculated using the information given by Best Buggies.
4		For Best Buggies:
5		Quarterly Payment Amount	2240
6		Total Period	5	Years
7		Number of Quarterly Payments (n)	=D6*4
8		Quarterly Interest Rate (i)	0.0372
9
10		Present Value of the payments will be the value of the car.
11		The present value of the payments can be calculated by finding the present value of annuity.
12
13		Present value of payments at Best Buggies	=Quarterly Payments*(P/A,i,n)
14			=D5*PV(D8,D7,-1,0)	=D5*PV(D8,D7,-1,0)
15
16		Hence value of car is	=D14
17
18		Data for California cars are as follows:
19		Monthly Payment	935
20		Total period	4	years
21		Number of monthly payments	=D20*12
22
23		Since value of car at both places are same, therefore the present value of
24		payments should be equal to the value of car calculated above.
25
26		Value of the car	=D16
27
28		The interest can be calculated as using rate function.
29		Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the interest rate as follows:
30		NPER	=D21
31		PMT	=D19
32		PV	=-D26
33		FV	0
34
35		Monthly Interest rate	=RATE(D30,D31,D32,D33)	=RATE(D30,D31,D32,D33)
36
37		Hence monthly interest rate is	=D35
38