PRAXIS: Applications of Integration – Compound Interest and Future Value of Income Streams

Compound Interest

1. Suppose you put $1000 into an account that yields 6% per year compounded daily. How much will you have after 5 year and after 20 years?
2. Suppose you put $150 into an investment account that has an annual rate of return of 10% per year, compounded quarterly. How much money will be in the account in 15 years and in 40 years?
3. Suppose you take out a loan against your life insurance policy worth $50,000. Given that you don’t have to make regular payments into the account, the account will simply accrue interest at a rate of 2.2% per year, compounded continuously. How much will you owe after 10 years of not making any payments?
4. Suppose you buy a Charsux latte on your very first day of college using your student loans. The interest rate on your student loans is 5.2% per year, compounded daily. Supposing also that you don’t make any payments on your student loans for all 4 years of college and that you spent $5.25 on that latte, how much would you have to pay for that latte after you graduate (after all that interest has accrued)?

Future Value of Income Streams

5. Suppose we find an investment account that has an annual interest rate of 7.2% that you put $30000 into initially. As long as you keep the $30000 in the account you receive a “member’s reward” of $1.20 per day that you choose to have automatically put back into the account. Let’s assume for simplicity that the account compounds interest continuously and that the payouts are continuous as well. How much will this account be worth in 10 years?
6. Suppose you are starting a new job and you decide to set up a retirement account. You decide to have $700 contributed to the account from your paycheck each month, and we will assume that the $700 contribution broken into daily mini-contributions (so we will assume continuous contributions for simplicity). If the retirement account has a rate of return of 5.35% on average, compounded continuously, how much is the account worth after 35 years?
7. Suppose you find an investment account that you decide to contribute to every month over the course of 30 years. The investment has an average rate of return of 5.2%, compounding daily. Also, you decide to start the account with an initial amount of $10,000, and that your monthly contributions will be $1000. How much is the account worth after 30 years? Suppose, for the sake of simplicity that the account compounds continuously, and that your contributions to the account are spread out evenly (continuously) over the course of the year.
8. There are basically no accounts or investments or debts that compound continuously, nor have a payout/contribution that is continuous. Why, then, is it usually reasonable to assume continuous compounding and continuous payout/contributions like we did in the last problem (aside from “it makes the math easier”)?