SOLUTION: You have an annuity at a fianacial instiution. the installments is yearly and the first installment of R 10 000 is payable at the end of the first year. the contract period is 20 y

Question 1085994: You have an annuity at a fianacial instiution. the installments is yearly and the first installment of R 10 000 is payable at the end of the first year. the contract period is 20 years. the payment escalates yearly with 10%. the capitalization rate is 12%, compounded yearly, what is the present value of the contract?
Found 2 solutions by Theo, JuanKoss:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
first installment is 10,000
each additional installment is multiplied by 1.10
that means your inflation rate is 10% per year.
your discount rate is 12% per year.

your effective discount rate is equal to (1 + dr) / (1 + ir) = 1.12 / 1.10 = 1.01818181818........ - 1 = .0181818181818 * 100% = 1.818181818.....%

one more adjustment needs to be made.

the first payment is 10,000 at the end of the first year.

when you use the composite discount rate, the payments need to be effective at the start of the analysis, which is at the beginning of year 1, also known at time point 0.

because of this, you need the annual payment to be equal to 10,000 / 1.10 = 9090.909091.

the calculator will tell you that the present value of annual payments of 9091.909091 for 20 years at the composite discount rate of 1.8181818...% per year is $151,290.92

the result of the calculation is shown below:

if you treat this as a cash flow problem, you will find that you get the same present value.

i used excel and this is what i got:

i also used excel to show you the difference between inflating the annual charges each year by 10% starting in time point 2 and then dividing by the discount rate of 12% to get the present value cash flows.

this is compared to finding the composite discount rate of (1.12/1.10 - 1) * 1005 = 1.8181818%, adjusting the 10,000 in time point 1 so that it will be equal to 10,000 in time point 1 after inflating by 10%, and then solving for the present value of cash flows using the composite discount rate.

the present value of cash flows is the same as it should be.

hopefully this makes sense to you.

if not, come back with questions and i'll try to answer as best i can.

Answer by JuanKoss(3) (Show Source): You can put this solution on YOUR website!
It is wery interesting! Thank you man!
RELATED QUESTIONS
A sum of 8550 is to be paid in 15 installments where each installment is 10'more than... (answered by DrBeeee)
A real estate company sells its premium house model at 2,500,00.00 Php. One can pay it in (answered by Theo)
You have ₱15,000 and wish to receive an annual annuity for 10 years. The annual... (answered by ikleyn)
The future value of an annuity is R 24 000. the monthly annuity is R 1000 and the annuity (answered by Theo)
Betty received $ 500,000 from a life insurance policy to be distributed to her as an... (answered by CPhill)
A vehicle is purchased on credit, divided into 11 monthly installments. The first month... (answered by ikleyn)
A man borrowed rs 500 from his friend and decided to return this amount in four equal... (answered by ikleyn)
An annuity bond has level payments (coupon plus redemption) every coupon period. Thus it... (answered by ikleyn)
A second-hand car was bought for ₱100,000 downpayment and monthly installments of... (answered by yurtman,ikleyn)