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RUDIKE [14]
2 years ago
12

suppose 7,500 is invested at 1.5%, compounded continuously. what will the account balance be in 16 years?​

Mathematics
1 answer:
viktelen [127]2 years ago
7 0

Answer:

\boxed {\boxed {\sf \$9,534.37}}

Step-by-step explanation:

The formula for continuously compounded is:

A=Pe^{rt}

where P is the principal amount, r is the interest rate as a decimal, and t is the amount of time.

The principal amount is $7,500 and time is 16 years. The interest rate is 1.5%. Convert this to a decimal- divide by 100 or move the decimal places two spots to the left.

  • 1.5/100= 0.015         or           1.5 --> 0.15 --> 0.015

Now we know all the values and can substitute them into the formula.

P= 7500 \\r= 0.015 \\t= 16

A= 7500(e^{0.015*16})

Solve the multiplication in the exponent first.

A= 7500(e^{24})

Solve the exponent.

A= 7500 (1.27124915)

A=9534.368627

Round to the nearest cent (hundredth place). The 8 in the thousandth place tells us to the round the 6 to a 7.

A=9534.37

The account balance will be <u>$9,534.37</u> after 16 years.

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