Question

You just borrowed $50,000 to buy a car. You will pay back this loan with monthly payments of $1,610 for 4 years. What is the APR (annual percentage rate) on this loan?

What is the effective annual rate associated with an 8% nominal annual rate (r = 0.08) when interest is compounded (1) annually: (2) semiannually: (3) quarterly: (4)monthly:

You negotiate a great deal and your bank agrees to lend you money for 30 years at 4% APR (annual percentage rate). The house costs $300,000 and you pay 20% down and finance the rest. (1) Monthly payment: (2) The interest payment portion of 1st Monthly payment: (3) The principal payment portion of the 1st Monthly payment: (4) Balance after the 1st payment:

You end up with $20,000 after investing for 20 years at 8% annually. What was the PV?

Answer 1

Answer :1 :

Calculation of Annual percentage rate :

Annual Percentage rate can be calculated using rate function of Excel :

=RATE(nper,pmt,pv,fv)

where nper is the number of payments i.e 4 * 12 = 48

pmt is the periodic payment i.e $1,610

pv is the loan amount i.e 50,000

fv is future value i.e 0

=RATE(48,1610,-50000,0)

The monthly percentage rate is 1.94%

The Annual percentage rate is 1.94%*12 = 23.27%

Answer : 2 Calculation of Effective Annual Rate :

Effective Annual rate = [(1 + r)^n - 1 ]

where r is the rate of interest per period

n is the number of compounding period

Effective annual rate when compounded annually :

Effective Annual rate = [(1 + 0.08)^1 - 1 ]

= [1.08 - 1]

= 0.08 or 8%

where r is the rate of interest per period i.e 0.08

n is the number of compounding period i.e 1

Effective annual rate when compounded semi annually :

Effective Annual rate = [(1 + 0.04)^2 - 1 ]

= [(1.04)^2 - 1]

= 0.0816 or 8.16%

where r is the rate of interest per period i.e 0.08/2 = 0.04

n is the number of compounding period i.e 1 * 2 = 2

Effective annual rate when compounded quarterly :

Effective Annual rate = [(1 + 0.02)^4 - 1 ]

= [(1.02)^4 - 1]

= 0.08243216 or 8.24%

where r is the rate of interest per period i.e 0.08 / 4 = 0.02

n is the number of compounding period i.e 1 * 4 = 4

Effective annual rate when compounded monthly :

Effective Annual rate = [(1 + 0.006667)^12 - 1 ]

= [1.083 - 1]

= 0.083 or 8.30%

where r is the rate of interest per period i.e 0.08/ 12 = 0.00666667

n is the number of compounding period i.e 1 * 12 = 12

Answer : 3 (1) Calculation of Monthly payment

=PMT(rate,nper,pv)

where rate is the rate of interest per period i.e 4% / 12 = 0.33333%

nper is the number of payments i.e 30 * 12 = 360

pv is the amount of loan i.e 240000 [300000 - (300000 * 20%)]

=PMT(0.3333%,120,-240000)

Monthly payment is 1145.80

(2) interest payment portion of 1st Monthly payment :

=IPMT(rate,per,nper,pv)

where rate is the rate of interest per period i.e 4% / 12 = 0.33333%

per is the 1st payment i.e 1

nper is the number of payments i.e 30 * 12 = 360

pv is the amount of loan i.e 240000 [300000 - (300000 * 20%)]

=IPMT(0.3333%,1,360,-240000)

interest payment portion of 1st Monthly payment is 800

(3) The principal payment portion of the 1st Monthly payment :

=PPMT(rate,per,nper,pv)

where rate is the rate of interest per period i.e 4% / 12 = 0.33333%

per is the 1st payment i.e 1

nper is the number of payments i.e 30 * 12 = 360

pv is the amount of loan i.e 240000 [300000 - (300000 * 20%)]

=PPMT(0.3333%,1,360,-240000)

interest payment portion of 1st Monthly payment is 345.80

(4) Balance after the 1st payment: = 240000 - 1145.80

= 238854.2

Answer : 4 Calculation of PV

Present value = Future value / [(1 + rate)^n]

= 20000 / [(1 + 0.08)^20]

= 20000 / 4.6609571

= 4290.9641