Savings institutions often state a nominal rate, which can be thought of as a simple annual interest rate, and the effective interest rate, which is the actual interest rate earned due to compounding. Given the nominal rate, it is easy to calculate the effective interest rate as follows. Assume that $1 is invested in an account paying an interest rate of 6% compounded monthly. Using the compound interest formulaUpper A equals Upper P left parenthesis 1 plus StartFraction r Over m EndFraction right parenthesis Superscript nA=P1+rmn, with P = 1, r = 0.06, m = 12, and n = 12,Upper A equals left parenthesis 1 plus StartFraction 0.06 Over 12 EndFraction right parenthesis Superscript 12 Baseline almost equals 1.0617A=1+0.061212≈1.0617.So the effective interest rate is 1.0617minus−1 = 0.0617, or 6.17%.
Find the effective interest rate for the investments with a nominal yield of 6 %6%, compounded daily.

Write an inequality and solve each problem. for exercises 11 and 12, interpret the solution.

Linda loans her friend $250 with a 5% monthly intrest rate. how much was the whole loan?

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?