A family paid $99,000 cash for a house. fifteen years later, the house was sold for $195,000. if interest is compounded continuously, what annual nominal rate of interest did the original $99,000 investment earn?

Question

Gavyn Thornton

Business

27 September, 23:08

A family paid $99,000 cash for a house. fifteen years later, the house was sold for $195,000. if interest is compounded continuously, what annual nominal rate of interest did the original $99,000 investment earn?

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Lexi Tyler · Answer 1

Starting with the continuous compound interest formula, we have A = Pe^rt where P is the principal amount to be invested, r is the rate of annual interest to be compounded continuously, t is the period of time in years for which the amount P invested, A is the total amount in the account at the end of time t.

Given that a family paid $99,000 cash for a house and it was sold for $195,000 after fifteen years. Now we have to find the annual nominal rate of interest did the original $99,000 investment earn if interest is compounded continuously. Substituting the values we have P=$99,000, A=$195,000, t = 15 years.

Hence, the equation above becomes 195,000 = 99,000e^r (15) = > e^r (15) = 195,000/99,000 = > e^r15 = 65/33.

ð Ln (e^r15) = ln (65/33) = > 15rln€ = 0.67788

ð R = 0.67788 / 15 = 0.045192 = 4.52%

The annual nominal rate of interest is 4.52%.