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Concept explainers
(a)
To find:The number of times per year the interest is compounded and the interest rate that is used to find the interest if amount is invested compounded quarterly.
(a)
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Answer to Problem 1MP
The interest is compounded 4 times per year and the interest rate used is 0.95% if amount is invested compounded quarterly.
Explanation of Solution
Given information:Theinitial amount invested is $15,820 at annual interest rate 3.8%. The bank calculates the rate if compounded quarterly is
Calculation:
There are 12 months in a year. Quarterly means every 3 months of a year.
If interest is compounded quarterly, then the interest earned is added to the principal amount every three months.
So, the number of times interest is compounded per year is:
The quarterly interest rate is
Therefore, the interest is compounded 4 times per year and the interest rate used is 0.95% if amount is invested compounded quarterly.
(b)
To find:The value of CD after one year and complete the given table.
(b)
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Answer to Problem 1MP
The value of CD after one year is $16,429.781 and the complete table with values is Table (1).
Explanation of Solution
Given information:The initial amount invested is $15,820 at annual interest rate 3.8%.
Formula used: The balance of an account if it earns compound interest is calculated by the formula:
Here, A is the balance, r is the annual interest rate, P is the principal amount, n is the number of times interest compounded per year and t is the times in years.
Calculation:
From part (a),
For Quarter 1:
To confirm the values given in the table, substitute 15820 for P , 0.095 for r , 1 for n and 1 for t in the above formula.
So, the ending principal is $15,970.29.
For Quarter 2:
To find the ending principal for quarter 2, substitute 15970.29 for P , 0.095 for r , 1 for n and 1 for t in the above formula.
So, the ending principal is $16122.0078.
The interest earned if principal amount is:
For Quarter 3:
To find the ending principal for quarter 3, substitute 16122.0078 for P , 0.095 for r , 1 for n and 1 for t in the above formula.
So, the ending principal is $16275.1669.
The interest earned if principal amount is:
For Quarter 4:
To find the ending principal for quarter 4, substitute 16275.1669 for P , 0.095 for r , 1 for n and 1 for t in the above formula.
So, the ending principal is $16429.781.
The interest earned if principal amount is:
The complete table is:
Quarter | Starting Principal | Interest Earned | Ending Principal |
1 | $15,820.00 | $150.29 | $15,970.29 |
2 | $15,970.29 | $151.7178 | $16,122.0078 |
3 | $16,122.0078 | $153.1591 | $16,275.1669 |
4 | $16,275.1669 | $154.6141 | $16,429.781 |
Table (1)
Therefore, the value of CD after one year is $16,429.781 and the complete table with values is Table (1).
(c)
To find:The simple interest earned onCD after one year.
(c)
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Answer to Problem 1MP
The simple interest earned on CD after one year is $601.16.
Explanation of Solution
Given information:The initial amount invested is $15,820 at annual interest rate 3.8%.
Formula used: The simple interest can be calculated by the formula:
Here, the principal is P , ttime in years and rate isr .
Calculation:
The annual interest rate is:
To find the interest, substitute 15820 for P , 3.8 for r and 1 for t .
Therefore, the simple interest earned on CD after one year is $601.16.
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High School Math 2011 Algebra 1 Student Companion Grade 8/9
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