what is the future value of an ordinary annuity of $12,000 per year,for three years at9% interest compounded annually?
To find out what your investment would be in 3 years, you must find the interest for year one and add it to the principle to find the interest for year two and so on. Which means your interest earns interest for you.
Principle x Rate=Interest
Year 1: 12,000 x .09 =1080
Year 2: 13,080 X .09 =1177.20
Year 3: 14,257 C .09 =1283.14
Now add up the interest
1080+ 1177.20+ 1283.14=3540.34
To find the Future Value add the interest plus your initial investment. 3540.34+ 12,000= $15,540.34
future amount = 12000(1.09^3
=15540.35
interest=principle*rate*time
i=12000*.09*1
begin each year by adding both interest from end of last year plus new annuity payment= to principle
12000 end of first period
25080 end of second period
39337.2 end of third period
39337.2=future value
To find the future value of an ordinary annuity, you can use the formula:
FV = P × (1 + r)^n - 1 / r
Where:
FV is the future value of the annuity
P is the annual payment
r is the interest rate per period
n is the number of periods
In this case, the annual payment is $12,000, the interest rate is 9%, and the number of periods is 3.
Let's calculate the future value using the formula:
FV = 12000 × (1 + 0.09)^3 - 1 / 0.09
First, calculate (1 + 0.09)^3:
(1 + 0.09)^3 = 1.09 × 1.09 × 1.09 = 1.295029
Now, substitute the values into the formula:
FV = 12000 × (1.295029 - 1) / 0.09
FV = 12000 × (0.295029) / 0.09
FV ≈ 39250.47
Therefore, the future value of the annuity is approximately $39,250.47.