# math

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Compute the compound quarterly amount after 1 year for \$100 invested at 12% interest compounded quarterly. What simple interest rate will yield the same amount in 2 years?

• math -

P = Po(1+r)^n.

r = (12%/4) / 100% = 0.03 = Quarterly %
rate expressed as a decimal.

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

a. P = 100(1.03)^4 = \$112.55.

b. P = Po + Po*r*t.

r = APR expressed as a decimal.
t = 2 Years.

100 + 100*r*2 = 112.55.
100*r*2 = 112.55 - 100 = 12.55.
r = 12.55 / 200 = 0.06275 = 6.275%.

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