Determine the sum of an annuity of P1,200 payable at the end of each month for 2 years. Money is worth 6% compounded monthly.
just plug your numbers into your handy annuity formula.
To determine the sum of an annuity, we can use the formula for the future value of an ordinary annuity:
\[FV = P \times \left(\frac{(1+r)^n - 1}{r}\right)\]
Where:
- FV = Future Value
- P = Payment/Annuity
- r = Interest rate per period
- n = Number of periods
In this case, the payment is P1,200, the interest rate is 6% compounded monthly, and the number of periods is 2 years (24 months).
First, let's determine the interest rate per period. Since the interest is compounded monthly, we divide the annual interest rate by 12:
\[r = \frac{6}{100} \div 12 = 0.005\]
Next, we can substitute the values into the formula:
\[FV = 1200 \times \left(\frac{(1+0.005)^{24} - 1}{0.005}\right)\]
Now, let's calculate the future value:
\[FV = 1200 \times \left(\frac{(1.005)^{24} - 1}{0.005}\right)\]
Using a calculator, the future value is approximately $30,024.65.
Therefore, the sum of the annuity of P1,200 payable at the end of each month for 2 years, with an interest rate of 6% compounded monthly, is approximately P30,024.65.
To determine the sum of an annuity, we can use the formula for the present value of an annuity.
The formula to find the present value of an annuity is:
PV = (PMT * [1 - (1 + r)^(-n)]) / r
Where:
- PV is the present value or the sum of the annuity
- PMT is the periodic payment (P1,200 in this case)
- r is the interest rate per compounding period (6% compounded monthly, so r = 6% / 12 = 0.005)
- n is the total number of compounding periods (2 years, and since payments are made monthly, the total number of periods is 2 * 12 = 24)
Now let's plug in the values into the formula:
PV = (1200 * [1 - (1 + 0.005)^(-24)]) / 0.005
Calculating this formula will give us the present value (sum) of the annuity.