Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

Question

Initial	InvestmentAnnual	% RateTime to	DoubleAmount After	10 Years
$1500
71
2	%	yr	$

Answer 1

the underlying formula that you want to use here for continuous compounding is

A = P*e^(rt)

for this scenario that means taking

A = 1500 * e^(0.07*10)

A = 3020.63

meaning that the accumulated amount in the account after 10 years is $3,020.63

then for the time to double you can take

t = ln(2) / r

t = ln(2) / 0.07 = 9.90 years

Answer 2

Use the formula

A = Pe^rt

where

P = Iniitial Investment

r= annual rate of interest

t = number of years

e = about 2.718281828

A= ending Amount continuously compounded at r interest rate for t years, with P=initial amount

plug in the values, use a calculator. Multiply P by e^rt

e^rt is the limit of (1+r/n)^nt as n approaches infinity

n= number of compounding periods per year

r= annual interest rate, t = years