Starting Out with C++: Early Objects
8th Edition
ISBN: 9780133360929
Author: Tony Gaddis, Judy Walters, Godfrey Muganda
Publisher: Addison-Wesley
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Textbook Question
Chapter 6, Problem 10PC
Present Value
Suppose you want to deposit a certain amount of money into a savings account and then leave it alone to draw interest for the next 10 years. At the end of 10 years you would like to have $10,000 in the account. How much do you need to deposit today to make that happen? To find out you can use the following formula, which is known as the present value formula:
The terms in the formula are as follows:
- P is the present value, or the amount that you need to deposit today.
- F is the future value that you want in the account (in this case, $10,000).
- r is the annual interest rate (expressed in decimal form, such as .042).
- n is the number of years that you plan to let the money sit in the account.
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Interest Rates Savings accounts state an interest rate and a compounding period. If theamount deposited is P, the stated interest rate is r, and interest is compounded m timesper year, then the balance in the account after one year is P⋅(1+rm)m. For instance, if$1000 is deposited at 3% interest compounded quarterly (that is, 4 times per year), thenthe balance after one year is1000⋅(1+.034)4=1000⋅1.00754=$1,030.34.Interest rates with different compounding periods cannot be compared directly.The concept of APY (annual percentage yield) must be used to make the comparison. TheAPY for a stated interest rate r compounded m times per year is defined byAPY=(1+rm)m−1.(The APY is the simple interest rate that yields the same amount of interest after oneyear as the compounded annual rate of interest.) Write a program to compare interestrates offered by two different banks and determine the most favorable interest rate. SeeFig. 4.24.
Chapter 6 Solutions
Starting Out with C++: Early Objects
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