Differential equation involving money

• angelgurlxo87
In summary, a recent college student borrowed $100,000 at an interest rate of 9% and expects to make monthly payments of 800*(1+t/120), where t is the number of months since the loan was made. The loan will be fully paid when the amount still owed, A(t), is equal to 0. This can be solved using a "difference" equation or a differential equation, depending on how the interest is accounted for. angelgurlxo87 A recent college student borrowed$100,000 at an interest rate of 9%. With salary increases, he expects to make payments at a monthly rate of 800*(1+t/120), where t is number of months since the loan was made.

(a.) Assuming that this payment schedule can be maintained, when will the loan be fully paid?

I figured that I would need to differentiate this equation (800*(1+t/120)), and i got:
(96,000)/(14,400) = 6.66

Your title refers to a differential equation but I see no differential equation here. Also I don't see where you have included the 9% interest. Assuming that is annual interest, that would be the same as 9/12= 3/4% per month. Each month the amount he must pay increases by 3/4% and decreases by 800(1+ t/120). I have no idea why you would want to differentiate that or what you set the derivative equal to. If we let A(t) be the amount still owed after t months, then the change, from month t to t+1, is $\delta$A= (1.0075) A(t)- 800(1+ t/120), giving you a "difference" equation to solve for A(t) and then solve A(t)= 0.

If you really intend using a differential equation, then we can "average" the amount he pays over the month. Also the interest of 9% per year, if we treat it as "compound continuously" becomes an amount of Ae0.09t. The differential equation is dA/dt= Ae0.09t- 800(1+ t/120). Solve that for A(t) (just integrate) and then solve A(t)= 0 for t.

1. What is a differential equation involving money?

A differential equation involving money is a mathematical equation that describes the rate of change of a financial quantity over time. It takes into account factors such as interest rates, inflation, and other economic factors.

2. Why are differential equations important in finance?

Differential equations are important in finance because they allow us to model and predict the behavior of financial systems over time. This helps with making informed decisions about investments, loans, and other financial transactions.

3. How are differential equations used in financial modeling?

Differential equations are used in financial modeling by creating mathematical models that represent the behavior of financial systems. These models can be used to predict future trends and make decisions about investments, risk management, and other financial strategies.

4. What types of financial problems can be solved using differential equations?

Differential equations can be used to solve a wide range of financial problems, such as determining the optimal time to invest in a stock, calculating the repayment schedule for a loan, or predicting the growth of a company's profits over time.

5. Do I need advanced math skills to understand differential equations involving money?

While a basic understanding of calculus and algebra is helpful, advanced math skills are not necessary to understand differential equations involving money. There are many resources available, such as online tutorials and textbooks, that can help explain the concepts in a more accessible way.

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