# Math

posted by Amanda

Find the effective rate corresponding to the given nominal rate. (Round your answer to the nearest hundredth of a percentage point.)
(a) 4%/year, compounded quarterly

? %

(b) 3%/year, compounded monthly

? %

1. Henry

P = Po(1+r)^n.

Po can be any amount, but it should be invested for one year.

a. Po = \$1.00. = Initial investment.

r = (4%/4) / 100% = 0.01 = Quarterly %
rate expressed as a decimal.

n = 4Comp/yr * 1yr = 4 Compounding
periods.

P = 1.00(1.01)^4 = \$1.0406.
Int. = \$1.0406 - \$1.00 = \$0.0406.
R=I/Po = (0.0406/\$1.00)*100% = 4.06%.

b. Po = \$1.00.
r = (3%/12) / 100% = 0.0025 = Monthly %
rate expressed as a decimal.

n = 12Comp/yr * 1yr = 12 Compounding
periods.

P = 1(1.0025)^12 = \$1.03042
I = \$1.03042 - \$1.00 = \$0.03042.
Rate = (0.0304/1.00) = 0.0304 = 3.04%.

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