Question

For 2 M Euros you can buy an annuity which lasts for 10 years. The expected return is 12%.

a) What annuity can you count on if the first periodic payment will be due in 1 year?

b) What annuity can you count on if the first periodic payment will be due in 4 year?

Answer 1

a)

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 2000000, i = Interest Rate = 0.12, n = Number of Periods = 10

Therefore,

2000000 = P*[1-{(1+0.12)^-10}]/0.12

240000 = P*0.67802676

Therefore, Annuity = P = 240000/0.67802676 = $353968.33

b)

Note: It is assumed the NUMBER OF ANNUITIES will be 10 i.e. After 4 years, 10 installments will be received.

FV of 2M after 3 years = 2000000*(1.12^3) = $2809856

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 2809856, i = Interest Rate = 0.12, n = Number of Periods = 10

Therefore,

2809856 = P*[1-{(1+0.12)^-10}]/0.12

337182.72 = P*0.67802676

Therefore, Annuity = P = 337182.71/0.67802676 = $497300.02