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Proficient level
Choosing a savings account with monthly compounding is more advantageous than one with annual compounding. Monthly compounding allows for the accumulation of more interest as it includes the interest earned in previous periods when calculating interest for subsequent periods. This leads to a higher overall future value.
Distinguished level
Borrowers prefer fewer compounding periods as it leads to lower interest accrual on the loan. With more frequent compounding, the loan balance increases, and interest is charged on the new balance. Opting for fewer compounding periods reduces overall interest accrual and potentially decreases the loan debt. BUS 3062 Unit 2 Assignment 2 Time Value of Money Annuity Cash Flows
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Proficient level
An amortization schedule is a table that provides a detailed breakdown of periodic loan payments, including the amount applied to principal and interest, as well as the remaining debt balance over the life of the loan. It is commonly used in various types of loans, such as mortgages or auto loans. The schedule allows borrowers to track their repayment progress, understand the composition of each payment, and determine the outstanding balance at any given time.
Distinguished level
Higher interest is incurred initially in the amortization period due to the higher outstanding principal balance. Initially, a larger portion of the payment covers interest, while less is allocated to reducing the principal. As the loan progresses, the principal balance decreases, leading to lower interest charges. Hence, the early stages of amortization have higher interest expenses.
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Proficient level
In the early years of a mortgage, the interest component of the payment provides a greater tax benefit than in the later years. Initially, a significant portion of the cost is allocated to interest, resulting in higher tax deductions. As the loan progresses, more of the price goes towards reducing the principal, reducing the tax-deductible interest amount. Therefore, the early years offer more substantial tax advantages through mortgage interest deductions. BUS 3062 Unit 2 Assignment 2 Time Value of Money Annuity Cash Flows
Distinguished level
Longer-term loans offer a greater tax benefit for interest because the initial years have higher interest payments. These extended loan periods allow for more years of tax deductions due to the continued presence of higher interest payments. The longer the loan term, the more significant the potential tax savings from mortgage interest deductions.
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Proficient level
The difference between an ordinary annuity and an annuity due lies in the timing of each payment relative to the period it covers. In an ordinary annuity, the charges occur at the end of each period. In contrast, in an allowance due, the prices are made at the beginning of each period.
Distinguished level
The future value of an annuity due is higher than an ordinary annuity because all payments are shifted back by one period. This adjustment provides an extra compounding period, leading to greater growth and a larger future value for the annuity.
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Proficient level
The future value of a $1,000 annuity payment over five years, with an interest rate of 9 percent,
is calculated as follows:
$900 x [(1+0.09)^5-1/0.09]
$900 x [1.5386-1/0.09]
$900 x [0.5386/0.09]
$900 x [5.98] = $5,386
Recalculating the future value at 8 percent interest and 10 percent interest:
At 8% interest:
$900 x [(1+0.08)^5-1/0.08]
$900 x [1.469-1/0.08]
$900 x [0.469/0.08]
$900 x [5.86] = $5,274
At 10% interest:
$900 x [(1+0.10)^5-1/0.10]
$900 x [1.610-1/0.10]
$900 x [6.10] = $5,490
Distinguished-level
Interest rate changes directly affect future values. Higher interest rates increase future deals as compounding growth is more significant. With higher speeds, the initial investment grows at a faster pace. Conversely, lower interest rates reduce future values, as compounding growth is slower. Thus, interest rate fluctuations have a direct impact on the future value of an investment. BUS 3062 Unit 2 Assignment 2 Time Value of Money Annuity Cash Flows
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Proficient level
The present value of a $800 annuity payment over six years, with an interest rate of 10 percent, is calculated as follows:
$700 x [1 – {1 / (1+0.10)^6} / 0.10]
$700 x [1 – {1 / 1.771561} / 0.10]
$700 x [(1 – 0.5644) / 0.10]
$700 x [0.4356 / 0.10]
$700 x [4.356] = $3,049.20
Recalculating the present value at 9 percent interest and 11 percent interest:
At 9% interest
$700 x [1 – {1 / (1+0.09)^6} / 0.09]
$700 x [1 – {1 / 1.677100} / 0.09]
$700 x [(1 – 0.596) / 0.09]
$700 x [0.404 / 0.09]
$700 x [4.488] = $3,141.60
At 11% interest
$700 x [1 – {1 / (1+0.11)^6} / 0.11]
$700 x [1 – (1 / 1.87041) / 0.11]
$700 x [(1 – 0.534) / 0.11]
$700 x [0.466 / 0.11]
$700 x [4.236] = $2,965.20
Distinguished-level
Interest rate changes affect present values inversely. Higher rates decrease present values by increasing the discounting factor, while lower rates increase present values by reducing the discounting factor. Thus, interest rate fluctuations directly influence the current value of an annuity, with higher rates reducing it and lower rates increasing it. BUS 3062 Unit 2 Assignment 2 Time Value of Money Annuity Cash Flows
