Mrs. Sandy expects to deposit $7,000 today into a daily savings account with ABC Bank. If the bank is currently offering an interest rate of 5.1% p.a., continuously compounded, how much will Sandy have in her bank account in 5 years? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Question
Mrs. Sandy expects to deposit $7,000 today into a daily savings account with ABC Bank. If the bank is currently offering an interest rate of 5.1% p.a., continuously compounded, how much will Sandy have in her bank account in 5 years? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
To solve this problem, we will use the formula for continuous compounding, which is:
A = P * e^(rt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) t = time the money is invested for, in years
Given: P = $7,000 r = 5.1% = 0.051 (in decimal) t = 5 years
Substituting these values into the formula, we get:
A = 7000 * e^(0.051*5)
Now, calculate the exponent first:
0.051 * 5 = 0.255
So, the equation becomes:
A = 7000 * e^0.255
Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.255:
e^0.255 = 1.290161119
So, the equation becomes:
A = 7000 * 1.290161119
Finally, calculate the multiplication:
A = $9021.13
So, Mrs. Sandy will have approximately $9021.13 in her bank account in 5 years.
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