Sarah invested $1000 in an account paying 5.5% interest compounded semi-annually. How long will it take for the account balance to reach $10,450?

it will take 43.25 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $1000

A = $10450

r = 5.5% = 5.5/100 = 0.055

n = 2 because it was compounded 2 times in a year.

Therefore,.

10450 = 1000(1 + 0.055/2)^2 × t

10450/1000 = (1 + 0.0275)^2t

10.45 = (1.0275)^2t

Taking log of both sides, it becomes

Log 10.45 = 2t log 1.0275

1.019 = 2t × 0.01178 = 0.02356t

t = 1.019/0.02356

t = 43.25 years

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

need more info

step-by-step explanation: