# calculus

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Suppose \$5000 is deposited in a bank account that compounds interest four times per year. The bank account contains \$9900 after 13 years. What is the annual interest rate for this bank account?

• calculus -

P = Po(1+r)^n.

r = Quarterly % rate.

n = 4 comp/yr + 13yrs = 52 = The # of
compounding periods.

9900 = 5000(1=r)^52.
(1+r)^52 = 9900 / 5000 = 1.98
Take Log of both sides:
52*Log(1+r) = Log1.98 = 0.296665
Log(1+r) = 0.00571.
1+r = 10^0.00571. = 1.013223.
r = 1.013223 - 1 = 0.013223 = Quarterly % rate.

APR = 4 * 0.013223 = 0.0529 = 5.29 %.
= Annual % rate.

• calculus -

thanks!

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