3.1. Annuities Flashcards
Annuities…
A series of cash flows that occur at the end of each period for some fixed number of periods.
Present value annuity…
Cash flow * (1/r - 1/r*(1+r)^n)
Or CF * PVAF(r,n)
Future value annuity…
Cash flow * (((1+r)^n-1)/r)
Or CF * FVAF(r,n)
Present value annuity due…
Cash flow * (1/r - 1/r*(1+r)^n) * (1+r)
Future value annuity due…
Cash flow * (((1+r)^n-1)/r) * (1+r)
An annuity pays £500 per year for 3 years. It yields 10%.
How much should be offered for the annuity…
Now, it drops to just £25 per month, paying 1.5% for a further 60 months.
How much should be reoffered for this…
500 * (1/0.1 - 1/0.1*(1+0.1)^3)
=£1,243.43
25 * (1/0.015 - 1/0.015*(1+0.015)^60)
= £984.51
A £30,000 mortgage will be paid over 25 years, in monthly installments.
The interest rate is 0.9%.
What is the monthly payment…
30,000/(1/0.009 - 1/0.009(1.009)^2512)
= £289.71
An individual saves £20,000 per year for 5 years, at 8% interest.
How much will they have to spend…
20,000*(((1+0.08)^5-1)/0.08)
=£117,332.02
A renter pays £400 per month, for 5 months, with the first payment due immediately.
The interest rate is 10%.
What is the value of this annuity due…
What is the future value of this annuity due…
400 * (1/0.1 - 1/0.1*(1.01)^5) * (1+0.1)
= £1,667.95
400 * (((1+0.1)^5-1)/0.1) * (1+r)
=£2,686.24
