In: Economics
After shopping for a car Amelia ended up borrowing $11000 from
her grandparents at 9% per year compounded annually with repayment
at the end of 5 years. Her Grandparents asked her to develop some
alternative repayment options.
If Amelia's TVOM is 11%, what is the present worth for Amelia of
each of the following 3 alternatives?
1) Interest only at the end of each year and principal at the end
of the fifth year. $
2) Equal annual payments. $
3) Pay the principal and interest in one lump sum after 5 years?
$
If Amelia's TVOM is 6%, what is the present worth for Amelia of
each of the following 3 alternatives?
1) Interest only at the end of each year and principal at the end
of the fifth year. $
2) Equal annual payments. $ .
3) Pay the principal and interest in one lump sum after 5 years?
$
IF TVOM=11%
Rate of intrest=9%
Intrest amount to be paid annually=0.09*11000=990
Present value factor=
where n= no. of years
End of year | Intrest paid(I) | Present value factor(PVF) | Present value(PV=I*PVF) |
1 | 990 | 0.9009 | 891.891 |
2 | 990 | 0.8116 | 803.484 |
3 | 990 | 0.7312 | 723.888 |
4 | 990 | 0.6587 | 652.113 |
5 | 990 | 0.5934 | 587.466 |
Total Intrest present value=3658.842
Now present value for the principal amount= principal amount*(PVF for 5th year)=11000*0.5934=6527.4
Total value=present value intrest+present value principal=6527.4+3658.842=10186.242
2) Equal annual installment
Installment=(11000/PVIFA(5yrs,11%))=11000/3.6959=2976.271
PVIFA(5yrs,11%) can be found from the present value of annuity table at 11% and 5 yrs. The image will be attached below.
End of year | Installment paid(I) | Present value factor(PVF) | Present value(PV=I*PVF) |
1 | 2976.271 | 0.9009 | 2681.322 |
2 | 2976.271 | 0.8116 | 2415.542 |
3 | 2976.271 | 0.7312 | 2176.250 |
4 | 2976.271 | 0.6587 | 1960.470 |
5 | 2976.271 | 0.5934 | 1766.120 |
Total value=sum of present value=10999.704
3)Intrest after 5 years=principal*((1+i)n-1)=11000*((1+0.09)5-1)=5924.863
Total amount to be paid=Intrest+principal=5924.863+11000=16924.8635
Present value=total amount*(PVF for 5th year)=16924.8635*0.5934=10043.214
When TVOM is changed to 6% the problem can be solved similar to above.
IF TVOM=6%
Rate of intrest=9%
Intrest amount to be paid annually=0.09*11000=990
Present value factor=
where n= no. of years
End of year | Intrest paid(I) | Present value factor(PVF) | Present value(PV=I*PVF) |
1 | 990 | 0.9434 | 933.962 |
2 | 990 | 0.88999 | 881.090 |
3 | 990 | 0.8396 | 831.204 |
4 | 990 | 0.7921 | 784.179 |
5 | 990 | 0.7472 | 739.728 |
Total Intrest present value=4170.163
Now present value for the principal amount= principal amount*(PVF for 5th year)=11000*0.7472=8219.2
Total value=present value intrest+present value principal=8219.2+4170.163=12389.363
2) Equal annual installment
Installment=(11000/PVIFA(5yrs,6%))=11000/4.21236=2611.363
PVIFA(5yrs,6%) can be found from the present value of annuity table at 6% and 5 yrs. The image will be attached below.
End of year | Installment paid(I) | Present value factor(PVF) | Present value(PV=I*PVF) |
1 | 2611.363 | 0.9434 | 2463.56 |
2 | 2611.363 | 0.88999 | 2324.087 |
3 | 2611.363 | 0.8396 | 2192.500 |
4 | 2611.363 | 0.7921 | 2068.461 |
5 | 2611.363 | 0.7472 | 1951.210 |
Total value=sum of present value=10999.818
3)Intrest after 5 years=principal*((1+i)n-1)=11000*((1+0.09)5-1)=5924.863
Total amount to be paid=Intrest+principal=5924.863+11000=16924.8635
Present value=total amount*(PVF for 5th year)=16924.8635*0.5934=12646.258