Compound Nomial Rate

Question

An initial $3800 investment was worth $4320 after one years and nine months. What quarterly compounded nominal rate of return did the investment earn? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

A = P(1+r/n)^nt

A = final amount = $4320

P = initial principal investment = $3800

r = interest rate as a decimal = to be found

n = # times compounded annually = 4  (quarterly)

t = time in years

 

For t we have 1 year and 9 months... 9 months = 9/12 years = .75 years

So t = 1.75 years

 

Plugging into the compound interest formula:

 

4320 = 3800(1+r/4)^4(1.75)   divide both sides by 3800

4320/3800 = (1+r/4)⁷

 

⁷√(4320/3800) = 1 + r/4

r/4 = ⁷√(4320/3800) - 1

r = 4[⁷√(4320/3800) - 1]

r = .0739637

 

r ≅ .0740 or 7.4%