20. RARE STAMPS Jeff Reschke bought a rare stamp for his collection. He agreed to pay a lump sum of $4000 after 5 years. Until then, he pays 6% simple interest every 6 months. (a) Find the amount of each semiannual interest payment. (b) Reschke sets up a sinking fund so that money will be available to pay off the $4000. He wants to make annual payments into the fund. The account pays 8% compounded annually. Find the amount of each payment into the fund. (c) Prepare a table showing the amount in the sinking fund after each deposit. (a) (b) Payment Amount of Interest Total in Number Deposit Earned Account
20. RARE STAMPS Jeff Reschke bought a rare stamp for his collection. He agreed to pay a lump sum of $4000 after 5 years. Until then, he pays 6% simple interest every 6 months. (a) Find the amount of each semiannual interest payment. (b) Reschke sets up a sinking fund so that money will be available to pay off the $4000. He wants to make annual payments into the fund. The account pays 8% compounded annually. Find the amount of each payment into the fund. (c) Prepare a table showing the amount in the sinking fund after each deposit. (a) (b) Payment Amount of Interest Total in Number Deposit Earned Account
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**20. RARE STAMPS**
Jeff Reschke bought a rare stamp for his collection. He agreed to pay a lump sum of $4000 after 5 years. Until then, he pays 6% simple interest every 6 months.
(a) Find the amount of each semiannual interest payment.
(b) Reschke sets up a sinking fund so that money will be available to pay off the $4000. He wants to make annual payments into the fund. The account pays 8% compounded annually. Find the amount of each payment into the fund.
(c) Prepare a table showing the amount in the sinking fund after each deposit.
| Payment Number | Amount of Deposit | Interest Earned | Total in Account |
|------------------|---------------------|----------------|------------------|
| | | | |
---
*Explanation:*
- **Semiannual Interest Payment Calculation (a):** Determine the amount paid every 6 months at a 6% simple interest rate.
- **Annual Payment into the Sinking Fund (b):** Calculate the regular payments needed to ensure $4000 is available after 5 years, considering an 8% annual compound interest.
- **Table (c):** This table will illustrate how the sinking fund grows with each deposit and the interest earned over time.
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