Show how you substitute the values into the formula, then use your calculator.

*Use A = P(1+r/n)nt to find the amount of money in an account after t years, compounded n times per year.
*Use I = Prt to find the amount of simple interest earned after t years

1) If a person invests $5780 in an account that pays 9% interest compounded annually, find the balance after 13 years.

I got A = 5780 (1+0.09/1)13, but my calculator answer doesn't seem right.

2) Find the value of $3500 deposited for 9 years in an account paying 5% annual interest compounded semi-annually.

3) Find the value of $1200 deposited for 18 years in an account paying 7% annual interest compounded monthly. I got A = 1200(1+.07/12)216, but again, I don't know how to use the calculator for this.

4) Find the amount of simple interest earned if you invest $9000 at .04% interest for 20 years. Then find the account balance.

1. Your expression is correct, I got 17720.35

(this might seem high, but true. Back in the "olden days" before calculators we used something called the rule of 72. It meant if you have a time and rate which multiplied to something close to 72, your money would double.
e.g. at 8% money would double in appr 9 years (9x8=72)
e.g. 100(1.08)^9 = 199.90
in your case it would have doubled in 8 years to appr. 11560 , which would reach 23120 after 18 years.
So 17720 after 13 years is reasonable.

2. amount = 3500(1 + .05/2)^(9(2))
= 3500(1.025)^18 = 5458.81

3. your expression is correct again, perhaps you don't know how to use your calculator

the magic key is the yx key

e.g. to do 4^3
enter 4
press the yx key
enter 3
press =

you should get 64

so for A = 1200(1+.07/12)^216

here are my keystrokes

.07 ÷12
=
+1
=
yx
216
= -------> at this point you should have 3.5125...
x
3500
=

you should get 12293.89

Sure, I can help you with that. Let's go through each question step by step and I'll explain how to substitute the values into the formula and use a calculator.

1) To find the balance after 13 years with an initial investment of $5780 and an annual interest rate of 9% compounded annually, we can use the formula A = P(1+r/n)^(nt). Let's substitute the values:
A = 5780(1+0.09/1)^(1*13)

To evaluate this expression on a calculator, you need to apply the exponent correctly. Here's how you can do it:
- Press the number '1' on your calculator.
- Add '0.09/1' to it. (Make sure to divide 0.09 by 1 to get the correct decimal value.)
- Press the equals '=' sign to get the result of the previous step.
- Raise the result to the power of '13', either by using the exponent key (^) or by multiplying the value by itself thirteen times.

This should give you the correct answer for the balance after 13 years.

2) For an initial deposit of $3500, an interest rate of 5% compounded semi-annually, and a time period of 9 years, we can use the same formula: A = P(1+r/n)^(nt). Let's substitute the values:
A = 3500(1+0.05/2)^(2*9)

Again, to evaluate this expression on a calculator, follow these steps:
- Press the number '1' on your calculator.
- Add '0.05/2' to it. (Divide 0.05 by 2 to get the correct decimal value for semi-annual compounding.)
- Press the equals '=' sign to get the result of the previous step.
- Raise the result to the power of '2*9'.

Calculate this expression correctly to find the value of the deposit after 9 years.

3) If you have an initial deposit of $1200, an interest rate of 7% compounded monthly, and a time period of 18 years, you can use the formula A = P(1+r/n)^(nt). Let's substitute the values:
A = 1200(1+0.07/12)^(12*18)

To evaluate this expression on the calculator, use the same steps as before:
- Press the number '1' on your calculator.
- Add '0.07/12' to it. (Divide 0.07 by 12 to get the correct decimal value for monthly compounding.)
- Press the equals '=' sign to get the result of the previous step.
- Raise the result to the power of '12*18'.

Make sure to calculate this expression properly to find the value of the deposit after 18 years.

4) To find the amount of simple interest earned from an investment of $9000 at an interest rate of 0.04% for 20 years, we can use the formula I = Prt. Substituting the values:
I = 9000 * 0.04% * 20

To calculate this on the calculator, follow these steps:
- Multiply '9000' by '0.04'. (Divide the percentage by 100 to get the decimal value.)
- Multiply the result by '20'.

This will give you the amount of simple interest earned over 20 years. To find the account balance, you can simply add the interest to the initial investment of $9000.

I hope this explanation helps you understand how to substitute values into formulas and use a calculator for these calculations.