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AVprozaik [17]
2 years ago
10

An amount of 45,000 is borrowed for 12 years at 4.25% interest, compounded annually. If the loan is paid in full at the end of t

hat period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Mathematics
1 answer:
alukav5142 [94]2 years ago
7 0

Answer:

The answer to your question is $79,749, to the nearest dollar.

Step-by-step explanation:

45 thousand dollars at 4.5 percent compounded annually for 13 years?

After one year the loan would accrue 4.5% interest, which is 0.045 times $45,000 dollars. Added to the base ($45000) this is (1 + 0.045)* $45,000, or $47,025. (Just over two thousand dollars interest.)

After two years we do this again with the new base, so it is $47,025 times (1.045), or $45,000 times (1.045) times (1.045) which can be written:

45000(1.045)2=49141.125  dollars.

You can see where this is going, I hope. After the thirteenth year we get:

45000(1.045)13≏79,748.8243759089  dollars.

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3 years ago
Help with 5b please . thank you.​
Allushta [10]

Answer:

See explanation

Step-by-step explanation:

We are given f(x)=ln(1+x)-x+(1/2)x^2.

We are first ask to differentiate this.

We will need chain rule for first term and power rule for all three terms.

f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x

f'(x)=(0+1)/(1+x)-(1)+x

f'(x)=1/(1+x)-(1)+x

We are then ask to prove if x is positive then f is positive.

I'm thinking they want us to use the derivative part in our answer.

Let's look at the critical numbers.

f' is undefined at x=-1 and it also makes f undefined.

Let's see if we can find when expression is 0.

1/(1+x)-(1)+x=0

Find common denominator:

1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0

(1-1-x+x+x^2)/(1+x)=0

A fraction can only be zero when it's numerator is.

Simplify numerator equal 0:

x^2=0

This happens at x=0.

This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.

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8 0
2 years ago
Step by step how to solve 4x+2=5(x+10)​
Shalnov [3]

Answer:

x = -48

Step-by-step explanation:

4x + 2 = 5(x + 10)

expand the 5(x+10)

4x + 2 = 5x + 50

-2 both sides

4x + 2 - 2 = 5x + 50 - 2

simplify

4x = 5x + 48

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4x - 5x = 5x + 48 - 5x

simplify

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÷ (-1) both sides

-x ÷ (-1) = 48 ÷ (-1)

simplify

x = -48

The answer is x = -48.

8 0
3 years ago
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