What is the present value (to the nearest whole pound) of a £1,250 payment, received annually, for 7 years, assuming that interest is compounded annually at 5%? £10,178£5,412£6,218£7,233£7,104
Question
What is the present value (to the nearest whole pound) of a £1,250 payment, received annually, for 7 years, assuming that interest is compounded annually at 5%? £10,178£5,412£6,218£7,233£7,104
Solution
The present value of an annuity can be calculated using the formula:
PV = Pmt * [(1 - (1 + r)^-n) / r]
where:
- PV is the present value
- Pmt is the annual payment
- r is the interest rate
- n is the number of periods
In this case:
- Pmt = £1,250
- r = 5% or 0.05
- n = 7 years
Substituting these values into the formula gives:
PV = £1,250 * [(1 - (1 + 0.05)^-7) / 0.05]
Calculating the expression in the brackets first:
= £1,250 * [(1 - (1.05)^-7) / 0.05]
= £1,250 * [(1 - 0.710681) / 0.05]
= £1,250 * [0.289319 / 0.05]
= £1,250 * 5.78638
= £7,233 (rounded to the nearest whole pound)
So, the present value of a £1,250 payment, received annually, for 7 years, assuming that interest is compounded annually at 5%, is approximately £7,233.
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