Question 5. A person established a trust on January 2, 2017 with $100,000 of bon

Question

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

The bond earns 5% of interest on its initial sum of 100,000$ per year; Also in following years, interest will be paid on what's left in the account after paying out 10,000$ each year on Jan 2nd;
Thus equation for the trust balance each year after accrual of interest and payment of 10,000$ is:
B0= 100,000 (1.05) - 10,000
Bn+1= Bn* (1.05) - 10,000

The trust will be depleted when for some 'k' Bk becomes <=0 ;

For an 8% interest rate per year:

B0= 100,000 (1.08) - 10,000
Bn+1= Bn* (1.08) - 10,000

The trust will be depleted when for some 'k' Bk becomes <=0 ;
  

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.