Question

You wish to buy a car for $12,000 at a 5% annual interest rate, compounded monthly. The loan will be repaid in 5 years with monthly payments. What is your monthly payment (calculated with the equations on the next page)? Compare your answer to that obtained with the built in function, PMT. Be sure to label all cells appropriately. (There is no need to create a monthly payment table, simply use the equations on the next page.)

Loans: where: and, interest due at the end of each month A = payment P = principal (amount of money) r repayment multiplier i annual interest rate (as a fraction, NOT as a percentage) m-number of compounding periods per year (usually 12 for house loans). n = total number of payments Investments (Present Value or Present worth): where: P- present value A payment out of the investment (can be interest, or interest and principal) /r capital recovery factor (or) present worth factor Excel Built-In Functions (The help windows in Excel provide additional explanation, also note the related built-in functions under the "financial" option button): Payment on a loan Present Value -PMT (rate, nper, pv, fv, type) PV(rate, nper, pmt, fv, type) CUMI PMT(rate, nper, pv, start-period, end-period, type) Cumulative Interest paid → where: rate annual rate /number of periods (i/m) nper total number of (compounding) periods pv = present value pmt payment fv future value (zero is the default) type = when is payment made (zero → end of period, I → beginning of period) start period first compounding period in which to make calculation (can be any except the last) end period last compounding period in which to make calculation (can be any except the first)

Answer 1

The monthly payment based on the formuae is below:
A=r*P
p=12000
r=(i/m)*((1+(i/m))^n)/(((1+(i/m))^n)-1)
i=5%
m=12
n=5*12=60
solving we get r=0.01887
Amount=12000*0.01887=226.45

using the pmt formuale in excel below:
=pmt(rate,nper,pv,fv,type)
rate=5%/12
nper=5*12=60
pv=-120000
fv=0
type=0
=pmt(5%/12,60,-12000,0,0)
=226.45
using pmt formulae or manual formulae the answers remain same