Question

a company that manufactures general-purpose transducers invested $2 million 4 years ago in high-yield junk bonds. if the bonds are now worth $2.8 million, what rate of return per year did the company make on the basis of (a) simple interest, and (b) compound interest? (c) what is the spreadsheet function to find the answer for compound interest?

Answer 1

The compound interest is 8.775%.

interest = p.

p is principal, i is the interest rate, and n is the periods. Inthis case, p is 2 and the interest is .8. (We can divide both sides by a million to make it simpler.) The number of periods is 4.

.8 = (2)(i)(4)

.8 = 8i

i = 10%. (solution)

Compound interest, again, is

interest = p [(1+r)^m - 1]

This time we can't cancel out the p by default. We must divide by 2if we want to avoid multiplying through. After doing so, we add 1to both sides.

1.4 = (1+r)^4

Log both sides.

log(1.4) = 4log(1+r)

log(1.4) / 4 = .0365 = log(1+r)

10^.0365 = 1 + r

1.08775 - 1 = r

r = 8.775%.

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