One salesperson has indicated that Mary\'s car loan requires payments of $200 pe
ID: 2755191 • Letter: O
Question
One salesperson has indicated that Mary's car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this two-year loan Mary has been approached by another salesperson to buy a new automobile with payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan's APR on Mary's car purchase You just won a lottery. The $1,000,000 prize will be paid to you over 10 years in equal annual payments. Is it better to take $750,000 today (assuming 10 per cent interest rate) or take the 10-year annuityExplanation / Answer
Formula for present value of an annuity = PV= A [ (1+k)n-1/k(1+k)n]
PV = Present value of fund
A = periodical instalments =
k=interest rate=12% pa=1% per month
n=periods=
The PV of first year payments =200*[(1.01)^12-1]/[0.01(1.01)^12]=200*11.25508=$2,251
The PV after one year for second year payments =400*[(1.01)^12-1]/[0.01*(1.01)^12]
=400*11.25508=$4,502
PV of the second year payments now =$4502/1.12=$4,019.671
So the PV of two year loan =$2251+$4019.67=$6,270.69
2. Formula for present value of an annuity = PV= A [ (1+k)n-1/k(1+k)n]
PV = Present value of fund=21000
A = periodical instalments =522.59/month
k=interest rate=k per month
n=periods=48 months
21000=522.59*[(1+k)^48-1]/k(1+k)^48
Factor PVIFA =21000/522.59=40.1844
From table k=0.75% per month =9% pa
So APR =9%
3. Formula for present value of an annuity = PV= A [ (1+k)n-1/k(1+k)n]
PV = Present value of fund=?
A = periodical instalments =100,000 per year
k=interest rate=10% pa
n=periods=10 yrs
PV = 100,000[(1.10)^10-1]/0.10(1.10)^10 =100,000*6.145 =$614,457
So PV of 10 year annuity is $614,517 (at 10% rate)
So it is better to take $75,000 today
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