Question

1. what quarterly deposits at the end of each quarter should be made into a savings account paying the nominal interest of 4% compounded quarterly to accumulate $10,000 at the end of 10 years?

2. Faith buys a used car by paying a $500 down payment plus $180 a month for 3 years. what was the price of the car if the interest rate on the loan is the nominal interest rate of 9% compounded monthly?

Answer 1

1. Quarterly Deposit = $ 204.56

2. Price of car = $ 6160.42

Working:

1. Calculation of Quarterly deposits

PARTICULARS	in formulae	VALUES
Rate of Interest Per annum		4.00%
Rate of Interest Per quarter	RATE	1.00%	=4%/4
Amount at End	FV	10000
Number of years		10
Number of quarters	NPER	40	=10*4
Quarterly Deposits	PMT	204.56
Formulae used		=-PMT(1%,40,0,10000,0)
		"=-PMT(RATE,NPER,PV,FV,TYPE)"

*PMT used in formulae is taken negative being cash outflow

*PV is taken zero, as no opening

*TYPE is taken '0' as amount is paid at the End of each period.

2. Calculation of Price of Car:

We first need to calculate the amount borrowed:

PARTICULARS	in formulae	VALUES
Rate of Interest Per annum		9.00%
Rate of Interest Per month	RATE	0.75%	= 9%/12
Amount of payments	PMT	180
Number of years		3
Number of Months	NPER	36	=3*12
Amount Borrowed	PV	$5,660.42
Formulae used		=-PV(0.75%,36,180,0,0)
		"=-PV(RATE,NPER,PMT,FV,TYPE)"

*PV used in formulae is taken negative

*FV is taken zero, as fully repaid

*TYPE is taken '0' as amount is paid at the End of each period.

Now,

Price of Car = Amount Borrowed + Down Payment

So,

Price of Car =5660.42 + 500 

Therefore, Price of Car = $ 6160.42

Therefore, Price of Car = $ 6160.42