1. Elizabeth is offered to buy a financial security that guarantees to pay her $
ID: 2771736 • Letter: 1
Question
1. Elizabeth is offered to buy a financial security that guarantees to pay her $10 every 2 years forever. The annual interest rate is 8%.
How much would she pay for it today if the first payment will be received today?
How much would she pay for it today if the first payment will be received in 1 year?
How much would she pay for it today if the first payment will be received in 2 years?
2.
Anna, Barbara and Clara have never been to Europe. So the three friends decided that 2 years from today they will take a graduation trip to Europe for the entire summer (3 months). For this trip, they decided to start saving money by depositing altogether $200 at the end of each month in their joint savings account that pays a special rate of interest of 12% per year (or 1% monthly). They will spend the entire saved amount during their summer trip.
How much money (fixed amount) will the three friends be able to withdraw from their joint savings account at the beginning of each of the three months of their European travel?
Explanation / Answer
Present value ofperpetual annuity is PV= c/r
Where c= annuity amount
R= interest rate per period of annuity.
Now interest rate is 8% pa= 16.64% per two years when compounded annually
So the PV =10/0.1664=60.10
So when the annuity is received today Elizabeth has to pay $60.10
If the first payment is received in 1 year she has to pay $60.10/1.08=$55.64
If the first payment is received after 2 years, she has to pay $60.10/1.1664=$51.52
Formula for future value of Annuity :
FV= A [ (1+k)n-1/k]
When A= $200
K=1%
N=no of periods =24 months
So FV= 200[{(1+0.01)24-1}/0.01]
=200(1.270-1)/0.01
=5,400
So Anna, Barbara and Clara will have $5400 for their summer trip of Europe and they can withdraw $1800 per month from joint savings account each month(assuming the investment is not earning further interest after 2 years)
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