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 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a $100,000 payment 30 years later
If an investor had purchased the security at market on March 28, 2020, and held it until it matured, she would have earned an annual rate of how much>> can anybody help me plz?
Can't answer without knowing the 2020 market price.
tuy
To calculate the annual rate of return for the investor who purchased the security on March 28, 2020, and held it until it matured on March 28, 2038, we can use the formula for compound interest.
Compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the initial investment)
r = the annual interest rate (unknown)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
Principal amount (P) = $24,099 (the price paid for each security on March 28, 2008)
Future value (A) = $100,000 (the promised payment on March 28, 2038)
Number of times compounded per year (n) = 1 (since there is no compounding mentioned, we assume it is compounded annually)
Number of years (t) = 30 (from March 28, 2008, to March 28, 2038)
We need to find the annual interest rate (r).
Rearranging the formula to solve for r:
r = (A/P)^(1/(n*t)) - 1
Now, let's plug in the values and calculate the annual rate of return:
r = ($100,000 / $24,099)^(1/(1*30)) - 1
r = 1.37639^(1/30) - 1
r = 1.0193 - 1
r = 0.0193 or 1.93%
Therefore, if an investor had purchased the security at market price on March 28, 2020, and held it until it matured on March 28, 2038, they would have earned an annual rate of approximately 1.93%.