To solve this, we can create an equation for the value based on time. So if we let t be the nmbers of years that have passed, we can create a function f(t) for the value in the savings account. 

We note that f(0) =5000. (We invest 5000 at time 0.) Next year, he will have 5% more than that. To find our total value at the end of the year, we multiply 5,000 * 1.05 = 5,250. f(1) = 5000(1.05)=5,250. At the end of year 2, we will have a 5% growth rate. In other words, f(2) = (1.05)* f(1). We can rewrite this as  . We can begin to see the proper equation is . If we plug in t = 15, we will have our account balance at the end of 15 years. So, our answer is .

The monthly rate is 

3 years = 36 months

According to the compound interest formula

and here , , , so we can plug into the formula and get the value

Calculate the total amount from each bank using the following formula:

Bank A:

Bank B:

Let  be the amount Bryan invested in the certificate of deposit. Then he deposited  in a savings account. 8% of the amount in the certificate of deposit is , and 3% of the amount in the savings account is ; add these interest amounts to get $365.00.  Therefore, we can set up and solve the equation:

Use the compound interest formula

substituting  (principal, or amount invested),  (decimal equivalent of the 8% interest rate),  (four quarters per year),  (one year).

Subtract 9,000 from this figure - the interest earned is $741.89

Since in each case the interest is compounded quarterly, the annual interest rate of 4% is divided by 4 to get 1%, the effective quarterly interest rate. 

The $10,000 remains in the savings account six months, or two quarters, so 1% is added twice - equivalently, the $10,000 is multiplied by 1.01 twice:

$5,000 is withdrawn from the savings account, leaving 

This money is untouched for six months, or two quarters, so again, we multiply by 1.01 twice:

Subtract $5,000 to get the interest:

12% annual interest compounded quarterly is, effectively, 3% interest per quarter.

Over the course of one quarter, Gary pays off , and the remainder of the loan accruses 3% interest. This happens four times, so we will subtract $2,400 and subsequently multiply by 1.03 (adding 3% interest) four times. 

First quarter:

Second quarter:

Third quarter:

Fourth quarter:

The thriteenth payment, with which Gary will pay off the loan, will be $913.16.

where  is the principal,  is the number of times per year interest is compounded,  is the time in years, and  is the interest rate.

Recall the formula for compound interest:

, where n is the number of periods per year, r is the annual interest rate, and t is the number of years.

Plug in the values given in the question:

For compound interest, the amount Nick owes is

where  is the principal, or starting amount of the loan ($1000),  is the interest rate per year (30% = .3). and  is the time that has passed since Nick took out the loan. (2)

We have

Hence our answer is $1690.