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3 years ago

Suppose that $18,000 is invested in a bond fund and the account grows to $23,344.74 in 5 yr.

Mathematics

1 answer:

emmainna [20.7K]3 years ago

4 0

Answer:

a. 5.2%

b. 9.8 years

Step-by-step explanation:

a. Put the given numbers in the formula and solve for r.

... 23,344.74 = 18,000×e^(r·5)

... 23,344.74/18,000 = e^(5r) . . . . . divide by 18000

... ln(1.29693) = 5r . . . . . . . . . . . . . . take the natural logarithm

... 0.26/5 = r = 0.052 = 5.2% . . . . . divide by 5

The rate of return is 5.2%, compounded continuously.

b. Put the given numbers in the formula and solve for t.

... 30,000 = 18,000×e^(0.052t)

... 30,000/18,000 = e^(0.052t) . . . . . divide by 18,000

... ln(5/3) = 0.052t . . . . . . take the natural log

... 0.510826/0.052 = t = 9.8 . . . . . divide by the coefficient of t

It will take 9.8 years for the investment to reach $30,000.

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