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(a) If $\$ 1000$ is invested at $8 \%$ per year compounded continuously (Exercise $46),$ what will the investment be worthafter 5 years?(b) If it is desired that an investment at $8 \%$ per year compounded continuously should have a value of $\$ 10,000$after 10 years, how much should be invested now?(c) How long does it take for an investment at $8 \%$ per yearcompounded continuously to double in value?

(a) $\$ 1491.82$(b) $\$ 4493.29$(c) 8.7 years

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS

Section 2

Separation of Variables

Integrals

Integration

Integration Techniques

Differential Equations

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we have $1000 in the bank and its gonna compounded continuously at 8%. And keep in mind that we previously were given the formula for an amount in the bank when it was compound and continuously be. It's the principle to what we start with. Arthuis, Interest rate and T is the time. First, let's figure the sexually should say $100 in 2000. Let's figure how much money we would have after five years. So we have a principal of 100. An interest rate of 8% sought to make that 80.8 in a time of five. So really, we're looking at 100 times E to the 0.4, which will work out to $149 in 18 cents. Next. We want to know how what we should have had in the bank if after 10 years we had $10,000. So now the new amount is 10,000. We have an unknown principle, an interest rate of 0.8 or 8% and a time of 10 years, so that would lead us to statement that 10,000 equals p times E to the 0.8 if we divide by E to the 0.8 we have the principle is 10,000 divided by E to the point which would give us a principle of 4000 $493 and 20 nine cents. Okay. And finally, we want to figure out how long it would take to double in amount. So let's say that we did start with $100. We double it, we're going to get to 200. We know the interest rate is 0.8 time of tea 200 divided by 100 is too. We will take the natural audible side, which would give us natural log to was national Augie to the 0.0 80 which is 800.0 80. So we will divide by the 0.8 We have natural log two divided by point eat, which will work out to be 8.66 years

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