SOLUTION: Suppose that over a six-year period ,1,000 dollars accumulated to 1,959 dollars in an investment certificate in which interest was compounded quarterly. (a)Find the nominal rate o

Question 1098349: Suppose that over a six-year period ,1,000 dollars accumulated to 1,959 dollars in an investment certificate in which interest was compounded quarterly.
(a)Find the nominal rate of interest, compounded quarterly, that was earned. (Round your answer to 2 decimal places.)
(b) Find the effective annual rate (EAR) rounded to 2 decimal places.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
number of quarters in a year is 4.
number of quarters in 6 years is 6 * 4 = 24

formula is f = p * (1+r)^n

f is the future value
p is the present value
r is the interest rate per time period (quarter of a year in this problem)
n is the number of time periods (quarters of a year in this problem).

formula becomes:

1959 = 1000 * (1+r)^24

divide both sides by 1000 and you get:

1959/1000 = (1+r)^24

take the 24th root of both sides of the equation to get:

(1959/1000)^(1/24) = 1+r

subtract 1 from both sides of the equation to get:

(1959/1000)^(1/24)-1 = r

solve for r to get r = .0284142874.

that's the interest rate per quarter.

the nominal annual interest rate is 4 * that = .1136571495 = 11.37% rounded to 2 decimal places

the effective annual interest rate is (1 + that)^4 - 1 = .118593795 = 11.86% rounded to 2 decimal places

not sure if you want the answer in percent interest rate or just interest rate.

answer i provided is in percent interest rate.

if you are interested in interest rate, then nominal is .11 rounded to 2 decimal places and effective is .12 rounded to 2 decimal places.

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