# compounded continously

Wnat to have \$60,000 in an account after 40 years. How much needs to be deposited inthe APR is 16.3% compounded daily?

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1. Compounded Continuously

Pt = Po*e^rt = \$60000,

r = (16.3%/365) / 100% = 0.0004466 = Daily % rate expressed as a decimal.

t = 40yrs * 365days/yr = 14600 days.

rt = 0.0004466 * 14600 = 6.52.

Po * e^6.52 = 60000,
Po = 60000 / e^6.52 = \$88.42 = initial deposit.

ComPounded Daily

Pt = Po*(1+r)^n = \$60000,
r = (16.3%/365) / 100% = 0.0004466 =
daily % rate express as a decimal.

n = 365comp./yr * 40yrs = 14600 comp.
periods.

Po*(1.0004466)^14600 = 60000,
Po = 60000 / (1.0004466)^14600 = \$88.52 = initial deposit.

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