Concept explainers
Lorri Morgan received $50 on her 16th birthday, and $70 on her 17th birthday, both of which she immediately invested in the bank, with interest compounded annually. On her 18th birthday, she had $127.40 in her account. Draw a time line, set up a polynomial equation, and calculate the YTM.
Answer to Problem 1EA
Solution:
Explanation of Solution
Given: $50 is invested in the first year and $70 is invested in the next year. The total amount after 2 years is $127.40.
Explanation:
Lorri Morgan invested $50 on her 16th birthday and $70 on her 17th birthday. On her 18th birthday, she had $127.40 in her account that pays interest compounded annually. The timeline for the given situation is as follows:
Assume that the interest is compounded annually at a rate
Use the compound interest formula:
The compounded amount of first investment of $50 in two years will be
The compounded amount of second investment of $70 in one year will be
The sum of two amounts is $127.40. So, the polynomial equation in
Assumingthat
Comparingthe above equation with quadratic equation
Use quadratic formula:
Take positive sign:
So, the value of
Conclusion: The polynomial equation for the calculation of YTM is
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