Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, RBMCC promised to repay the owner of one of these securities $92306 on March 28, 2049, but investors would receive nothing until then. Investors paid RBMCC $24507 for each of these securities; so they gave up $24507 on March 28, 2008, for the promise of a $92306 payment in 2049. Suppose that, on March 28, 2022, this security’s price is $45897. If an investor had purchased the security at market on March 28, 2022, and held it until it matured, what annual rate of return would she have earned? (Enter your answer as a percentage, omit the "%" sign in your response, and round your answer to 2 decimal places. For example, 0.12345 or 12.345% should be entered as 12.35.)
| We can use either the FV or the PV formula. | ||||||
| Both will give the same answer since they are the inverse of each other. | ||||||
| We will use the FV formula | ||||||
| FV formula, that is: FV = PV(1 + r)tSolving for r, we get: r = (FV / PV)1 / t– 1 | ||||||
| a. | ||
| PV=92306/(1+r)^41 | ||
| 24507=92306/(1+r)^41 | ||
| r=(92306/24507)^1/41-1 | ||
| r= | 3.29% | |
| b. | ||
| PV=45897/(1+r)^14 | ||
| 24507=45897/(1+r)^14 | ||
| r=(45897/24507)^1/12-1 | ||
| r= | 4.58% | |
| c. | ||
| PV=92306/(1+r)^27 | ||
| 45897=92306/(1+r)^27 | ||
| r=(92306/45897)^1/-1 | ||
| r= | 2.62% | |
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