suppose ana is an avid reader and buys only mystery novels. ana deposits $1,000 in a bank account that pays an annual nominal interest rate of 5%. assume this interest rate is fixed—that is, it won't change over time. at the time of her deposit, a mystery novel is priced at $10.00.
a) How much interest will Ana earn in a year?
Using the simple interest formula, we can calculate the interest earned in a year as:
Interest = Principal x Rate x Time
Where Principal is the amount deposited, Rate is the nominal interest rate, and Time is the number of years. So, we have:
Interest = 1,000 x 0.05 x 1
Interest = $50
Therefore, Ana will earn $50 in interest in a year.
b) How many mystery novels can Ana buy with the interest earned in a year?
If a mystery novel costs $10, we can divide the interest earned by the cost of a book to find out how many books Ana can buy. So, we have:
Number of books = Interest earned / Cost of one book
Number of books = $50 / $10
Number of books = 5
Therefore, Ana can buy 5 mystery novels with the interest earned in a year.
To solve the given problem, we can follow these steps:
1. Calculate the annual interest earned on the deposit.
2. Determine the number of mystery novels Ana can buy with the interest earned.
3. Find out the total number of mystery novels Ana can buy with her initial deposit and the interest earned.
Step 1: Calculate the annual interest earned on the deposit.
Given:
Principal (initial deposit) = $1,000
Nominal interest rate = 5%
To calculate the annual interest earned, we can use the formula:
Interest = Principal * (Nominal interest rate / 100)
Substituting the given values:
Interest = $1,000 * (5 / 100)
Interest = $1,000 * 0.05
Interest = $50
So, Ana earns $50 in interest annually.
Step 2: Determine the number of mystery novels Ana can buy with the interest earned.
Given:
Price of one mystery novel = $10.00
Interest earned annually = $50
To calculate how many mystery novels Ana can buy with the interest earned, we can divide the interest by the price of one mystery novel:
Number of mystery novels = Interest earned / Price of one mystery novel
Number of mystery novels = $50 / $10.00
Number of mystery novels = 5
So, Ana can buy 5 mystery novels with the interest earned.
Step 3: Find out the total number of mystery novels Ana can buy with her initial deposit and the interest earned.
To calculate the total number of mystery novels Ana can buy, we need to add the number of mystery novels she can buy with her initial deposit to the number of mystery novels she can buy with the interest earned:
Number of mystery novels (total) = Number of mystery novels (initial deposit) + Number of mystery novels (interest earned)
Number of mystery novels (total) = 0 + 5
Number of mystery novels (total) = 5
So, Ana can buy a total of 5 mystery novels with her initial deposit and the interest earned.