An investor wants to purchase an annuity that will pay her £80,000 per year for the next 10 years. If the constant, annual effective interest rate is 2%. How much should she be willing to pay today for the annuity? Answer to the nearest pound.

£718,607

Explanation:

Annuities are investment opportunities that require an initial settlement  and gives  a series of returns of a fixed amount for a specific number of periods.

In simple terms, the question requires us to calculate the amount to be paid today (Present Value) of an annuity that pays £80,000 per year for the next 10 years.

To establish the [Present Value of the Annuity, the future Cash Flows must be discounted to the Present Value using the appropriate discount rate. In our case, we will use the annual effective interest rate of 2%.

Present Value = PMT × [ 1 - 1/(1+r)^n ÷ r ]

Where,

PMT = £80,000

n = 10

r = 2%

Therefore,

Present Value = £80,000 × [ 1 - 1 / (1.02) ^ 10 ÷ 0.02]

                         = £718,606.80 or £718,607

Conclusion :

She be willing to pay £718,607 today for the annuity.

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explanation:

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