Question 5. A person established a trust on January 2, 2017 with $100,000 of bon
ID: 3167527 • Letter: Q
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Question 5. A person established a trust on January 2, 2017 with $100,000 of bonds that earn interest of 5% per year. The trust makes annual payments of $10,000 each January 2 starting next January until it is depleted. What is the equation for the trust balance each year? For how many years will the trust be able to make the full payout and how much will be left to pay out in its final year? What is the total amount that the trust paid out? If the trust held bonds that earned interest payments of 8% per year, how long would it be able to make payments and what total amount would the recipients receive?Explanation / Answer
Bonds amount borrowed = $100,000
Interest rate = 5% per year
Interest amount each year= 5/100 * 100,000 = $5,000
Interest amount for n years = $5,000 * n
Trust payment annualy =$10,000
Trust payment for n years = $10,000 * n
Total amount in excess of interest paid for n years = $(10,000 * n - 5,000 * n)= $5,000*n
Trust balance equation = $(100,000-5,000n)
Number of years for full payout is 100,000 - 5,000n=0
5,000n=100,000
n=20 years
Amount paid in final year= $(5,000 * 20 - 5,000 * 19)
=$5,000
Total amount paid by the trust = Principal borrowed + total Interest
$100,000 + $5,000* 20 = $200,000
If the Interest payments = 8% per year
Interest paid each year = 8/100 * 100,000 = $8,000
so, Trust balance equation = $ 100,000- n * (10,000 - 8,000)= $(100,000-2,000n)
Number of year for repayment= 100,000-2,000n=0
100,000=2000n
n=50years
Total amount recipients receive = Principal Borrowed + Total Interest paid
$(100,000 + 8,000 * 50) = $500,000
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