A sum of $850 is invested for 10 years and the interest is compounded quarterly. There is $1100 in the account at the end of 10 years. What is the nominal annual rate?

Answer 1

P = Po(1+r)^n.

Po = $850, r = Quarterly % rate expressed as a decimal.

n = 4Comp./yr. * 10yrs. = 40 Compounding periods.

P = 850(1+r)^40 = 1100,
(1+r)^40 = 1100/850 = 1.294,
Raise both sides to the 1/40 power: 1+r = 1.294^(1/40) = 1.00647, r = 1.00647 - 1 = 0.00647 = Quarterly % rate expressed as a decimal.

APR = 4 * 0.00647 = 0.0259 = 2.59 %.