# 1 Elizabeth is offered to buy a financial security that guarantees to pay her

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%.

(a)How much would she pay for it today if the first payment will be received today?

(b)How much would she pay for it today if the first payment will be received in 1 year?

#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?

(c)How much would she pay for it today if the first payment will be received in 2 years?

Explanation / Answer

Question 1a. 10 = Ax (1.08^2-1) A = 10/(1.08^2-1) Hence A = 60.10 Question 1b. After 1 year value of the security today must be $10+60.10=70.10 Hence after 1 year at 8% interest, A = 70.10/1.08 Therefore A = 64.90 Question 1b. If she get $10 now and $10 after every 2 year, Price of the security = $10+60.10=70.10 Question 2. No of period = 2*12 =24 First deposit is after 1 month. Therefore total deposit will be 2x12-1=23 deposit Formula for monthly compound interest is A = P x (1+1/100)^23 Here P =200 x 3 = $600 Or A = 600 x (1+01)^23+ 600 x 1.01^22 + ……………+ 600x1.01^2+ 600x1.01^1+ 600x1.01^0 or 600 x (1+01^23+ 1.01^22 + ……………+ 1.01^2+ 1.01^1+ 1.01^0) Or, A = 600 x (1.01^23-1)/(1.01-1) Or A = 600 x 0.257163/0.01 Therefore A = $15,429.78 Answer: $15,429.78 Sum of a series like a^n+a^(n-1)…………to n terms is (a^n-1)/(a-1) where a >1

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