In Chapter 1 of the text we looked at calculating a monthly payment for a loan.
ID: 3034706 • Letter: I
Question
In Chapter 1 of the text we looked at calculating a monthly payment for a loan. A related formula is to calculate the amount accruing when regular payments are made into an interest bearing account - often called the Savings Plan formula. (A is the accrued amount after t years of making regular payments, PMT, into an account at interest rate, r%, compounded n times each year.)
Suppose you want to buy a car and have decided that you can save $100 a month. Using information from an internet source, determine the current interest rate on savings accounts and use the information to answer the following: How much money will you have saved in a year’s time? How much will be interest? Why wouldn’t a linear model work here?
A(t) PMT ((1+ N-t 1 (v)Explanation / Answer
The Savings interest Rate is: 0.03% (California);
Source: https://www.bankofamerica.com/deposits/bank-account-interest-rates.go
A(t = 1yr)= 100*[(1+0.03%/12)^12 - 1]/(0.03%/12)
A(t=1yr) = 1200.165 ..... [Amount Saved in a year]
Interest = 16.5 cents
Linear Model wont work as interest is paid out monthly. So for the second month, the interest is paid not on 100+ 100 but 100 (1st month's PMT)+ interest(1st month) + 100 (2nd month's PMT)