# Determine the present value of \$9,500 in 12 years if money earns 4.1% per annum compounded quarterly.

To calculate the end amount of an investment made at a particular interest rate compounded a set number of times per year over a particular number of years, use the following formula:

`A=P(1+r/n)^(nt)`

To calculate the value of an investment, we need to begin with a formula:

`A=P(1+r/n)^(nt)`

Let's identify each of these variables. “A” is what we are seeking, the end amount or present value of the investment. “P” is the principle, the beginning investment. We identify “r” as the interest rate, and it must be expressed as a decimal. The variable “n” is the number of compoundings per year, and “t” is the number of years the investment is in place.

With this formula in place, let's try an example. Someone invests \$1,000 at a 3.5% interest rate per annum. The interest is compounded quarterly, and the investment lasts for ten years. Let's find the end amount.

Now we plug these numbers into our formula:

`A=1000(1+(0.035/4))^40`

We are seeking A. P equals 1000 (the initial investment); r is the interest rate, expressed as the decimal 0.035. The variable n is 4 because the interest is compounded four times per year (quarterly), and t is 10 for ten years. Multiplied together, they equal 40, so the exponent in the formula is 40.

When we calculate the result, we must be careful to follow the order of operations: parenthesis, exponents, multiply/divide, add/subtract. So we calculate within the parentheses, first dividing 0.035 by 4 and then adding 1. Then we raise the result by the exponent 40 (4 times 10). Then we multiply by 1,000. When we do this, we discover that A equals \$1,416.91. This is the amount of the investment of \$1,000 at 3.5% interest compounded quarterly after ten years.

Now plug the numbers from the original problem into the formula to find the end amount in that scenario.