Calculation of Annuity

An annuity consists of 8 annual payments of $1400 each, with the first payment being made at the end of 5 years. We need to find the amount of this annuity if the money is worth 7% per annum compounded annually.

Formula for Annuity Calculation

The formula for calculating the present value of an annuity is:

PV = Pmt x [(1 - (1 + r)^-n) / r]

Where PV = Present Value, Pmt = Payment per period, r = Interest rate per period, and n = Number of periods.

Calculation of Present Value

Using the above formula, we can calculate the present value of the annuity as follows:

Pmt = $1400
r = 7% per annum compounded annually = 0.07
n = 8 years

PV = $1400 x [(1 - (1 + 0.07)^-8) / 0.07]
PV = $1400 x [(1 - 0.5084) / 0.07]
PV = $1400 x [10.2835]
PV = $14,398.90

Explanation of the Calculation

The present value of an annuity is the sum of all the future payments discounted to their present value. In this case, we have a total of 8 annual payments of $1400 each. The first payment is made at the end of 5 years, and the payments continue for the next 7 years.

To calculate the present value of the annuity, we use the formula mentioned above. We plug in the values of the payment per period, the interest rate per period, and the number of periods. The formula gives us the present value of the annuity, which is $14,398.90.

Conclusion

Therefore, the amount of the annuity is $14,398.90. This means that if we invest $14,398.90 today, we will receive 8 annual payments of $1400 each, starting from the end of the 5th year, and the last payment will be made at the end of the 12th year.