A sum of $850 is invested for 10 years and the interest is compounded quarterly. There is $1050 in the account at the end of 10 years. What is the nominal annual rate?
+23248 The compound interest formula is: A = P(1 + r/n)^(nt)
where A = final amount, P = amount invested, r = decimal interest rate, n = number of times compounded per year, and t = number of years.
Entering the given values: 1050 = 850(1 + r/4)^(4*10)
---> 1050 = 850(1 + r/4)^40 Divide bothsides by 850, to get:
---> (1050/850) = (1 + r/4)^40 Find the 40th root of both sides, to get:
---> (1050/850)^(1/40) = 1 + r/4 Subtract 1 from both sides, to get:
---> (1050/850)^(1/40) - 1 = r/4 Multiply both sides by 4 to get:
---> [ (1050/850)^(1/40) - 1 ] * 4 = r
r ≈ .02119 --> r ≈ 2.119%
+23248 The compound interest formula is: A = P(1 + r/n)^(nt)
where A = final amount, P = amount invested, r = decimal interest rate, n = number of times compounded per year, and t = number of years.
Entering the given values: 1050 = 850(1 + r/4)^(4*10)
---> 1050 = 850(1 + r/4)^40 Divide bothsides by 850, to get:
---> (1050/850) = (1 + r/4)^40 Find the 40th root of both sides, to get:
---> (1050/850)^(1/40) = 1 + r/4 Subtract 1 from both sides, to get:
---> (1050/850)^(1/40) - 1 = r/4 Multiply both sides by 4 to get:
---> [ (1050/850)^(1/40) - 1 ] * 4 = r
r ≈ .02119 --> r ≈ 2.119%
