Basic math!please help!!!!?

Question

An ivestment of $500 000 is made which earns 7,5 % per year. If interest is compounded continuously:

A)determine the exponential function which states the compound amount S as a function of years of investment t

B)what will the $500 000 grow to its invested 10 years?20 years?

2.an investment $ 1 million which earns interest at the rate of 8,5 % per year is made. If interest is compounded continuously

A)what will the investment grow to

If it is invested for 10 years?25?

B)how long will it take for the investment to increase by 50%?

Answer 1

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Problem 1

The formula for continuously compounded interest is

A = Pe^rt, where P is the principal and r is the interest rate

In this case, we get A = 500000*e^(.075t)

To find the amounts after 10 or 20 years, substitute those values for t

Problem 2

Part A is the same type as 1A

To find the number of years required for a 50% increase, we want to find when the exponential on the right hand side of the equation equals 1.5.

1.5 = e^(.085t)

Take the natural log of both sides.

ln(1.5) = .085t

t = ln(1.5)/.085 = 4.77 years

Answer 2

for continuous compound , use formula

S=Pe^(rt)

P=500

r=0.075

t= year

then let t= 10

plug in solve for S

do the same for other question.