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Annual rate of return

Referring to the TMCC security story: (I don't think I am able to come close to the right answer here. I need help with this problem.)

"Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to repay the owner of one of these securities \$100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC \$24,099 on March 28, 2008, for the promise of a \$100,000 payment 30 years later. Such a security, for which you pay some amount today in exchange for a promised lump sum to be received at a future date, is about the simplest possible type. Is giving up \$24,099 in exchange for \$100,000 in 30 years a good deal? On the plus side, you get back about \$4 for every \$1 you put up. That probably sounds good; but on the down side, you will have to wait 30 years to get it."

Question:
Based on the \$24,099 price, what rate was TMCC paying to borrow money?
Suppose that, on March 28, 2020, this security's price is \$38,260. If an investor had purchased it for \$24,099 at the offering and sold it on this day, what annual rate of return would she have earned?
If an investor had purchased the security at market on March 28, 2020, and held it until it matured, what annual rate of return would she have earned?

Solution Preview

Based on the \$24,099 price, what rate was TMCC paying to borrow money?

Use the compound interest formula to calculate the rate. PV = 24,099, FV = 100,000 and the time period is 30 years
FV = PV (1+rate)^n
100,000 = ...

Solution Summary

The solution explains how to calculate the annual rate of return on a security

\$2.19