Carmen is acing for a new car that costs $15,000. If she puts $5000 in an account that earns 6% compounded monthly, how long will it take her to save enough money to buy the car?

it will take 18 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 = 5000

A = 15000

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

Therefore,.

15000 = 5000(1+0.06/12)^12× t

15000/5000 = (1.005)^12t

3 = (1.005)^12t

Taking the log of both sides,

Log 3 = log (1.005)^12t

0.4771 = 12t log1.005 = 12t × 0.0022

0.0264t = 0.4771

t = 0.4771/0.0264t

t = 18

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: