Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the following questions.
A. How much will be in the account after 3 years?
Show your work
B. How much will be I the account after 17 years?
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C. How many years will it take the account to contain $2000?
Show your work
D. How many years will it take the account to contain $2500?
Show your work
A. To calculate the amount in the account after 3 years, we use the formula for compound interest:
A = P(1 + r)^n
where:
A = amount in the account after n years
P = initial deposit (principal) = $1500
r = annual interest rate = 0.05
n = number of years = 3
Plugging in the values, we get:
A = $1500(1 + 0.05)^3
A = $1500(1.05)^3
A = $1500(1.157625)
A = $1736.44
Therefore, the amount in the account after 3 years will be $1736.44.
B. To calculate the amount in the account after 17 years, we use the same formula:
A = $1500(1 + 0.05)^17
A = $1500(1.05)^17
A = $1500(2.01359)
A = $3020.39
Therefore, the amount in the account after 17 years will be $3020.39.
C. To calculate how many years it will take for the account to contain $2000, we can set up the formula:
$2000 = $1500(1 + 0.05)^n
2000/1500 = (1.05)^n
1.3333 = (1.05)^n
Taking the natural log of both sides and solving for n:
ln(1.3333) = n * ln(1.05)
n = ln(1.3333) / ln(1.05)
n ≈ 3.88
Therefore, it will take approximately 3.88 years for the account to contain $2000.
D. To calculate how many years it will take for the account to contain $2500, we set up the formula:
$2500 = $1500(1 + 0.05)^n
2500/1500 = (1.05)^n
1.6667 = (1.05)^n
Taking the natural log of both sides and solving for n:
ln(1.6667) = n * ln(1.05)
n = ln(1.6667) / ln(1.05)
n ≈ 6.14
Therefore, it will take approximately 6.14 years for the account to contain $2500.