complete the table assuming continuously interest

Question

Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.)

Initial	InvestmentAnnual	% RateTime to	DoubleAmount After	10 Years
$900	%
93
5	yr	$

Answer 1

If this is right, then we can determine the answers according to the formula for continuous interest:

A = Pe^rt

Where:

A = Amount accumulated ($)

P = Starting principle ($)

e = natural exponential function (~2.718)

r = Interest rate (%)

t = Time (yrs.)

This formula can be used to calculate the last column - after 10 years, where P = 900, r = 5% (0.05), t = 10

A = 900e^0.05(10)

A = $1,483.85

To determine time to double, solve equation for t,

A = Pe^rt

e^rt = A/P

rt = ln(A/P)

t = [ln(A/P)]/r

where A = 2P (Doubled), r = 0.05

t = [ln(2P/P)]/0/05

t = ln2/0.05

t = 13.86 yrs.