Posted by **Amanda** on Friday, November 23, 2012 at 11:24am.

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

? %

- Math -
**Henry**, Friday, November 23, 2012 at 9:28pm
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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