Final answer:
The future value of ordinary annuities can be calculated using the annuity formula which factors in the regular payment amount, the interest rate, and the number of periods. By plugging values specific to each scenario—yearly payments, interest rate, and duration, we can compute the future value for each annuity presented in the question.
Step-by-step explanation:
The calculation of the future value of ordinary annuities involves determining how much a series of equal payments made at regular intervals will be worth at a future date when interest is compounded at a certain rate. This typically requires using the future value annuity formula, which is:
Future Value of Annuity = Payment × [× ((1 + r)^n - 1) / r]
where:
- Payment is the amount of the regular payment,
- r is the interest rate per period, and
- n is the number of periods.
Let's apply this formula to each scenario:
- £430 a year for 12 years compounded annually at 6 percent.
- €56 a year for 8 years compounded annually at 8 percent.
- $75 a year for 5 years compounded annually at 3 percent.
- £120 a year for 3 years compounded annually at 10 percent.
We will plug in the values for Payment, r, and n into the annuity formula for each of the scenarios above to find the future value for each annuity.
For example, for the first scenario:
Future Value of Annuity = 430 × ((1 + 0.06)^12 - 1) / 0.06
This pattern follows for each given annuity with their respective interest rates and time periods.