Max and Danielle deposit $500.00 into a savings account which earns 1% interest compounded quarterly. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?Use the formula A=P1+rnnt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.$
Question
Max and Danielle deposit
Solution
To solve this problem, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Given: P = $500.00 r = 1% or 0.01 (in decimal) n = 4 (since the interest is compounded quarterly) t = 3 years
Substitute these values into the formula:
A = 500(1 + 0.01/4)^(4*3)
Now, calculate the expression inside the parentheses:
A = 500(1 + 0.0025)^(12)
A = 500(1.0025)^(12)
Now, calculate the exponent:
A = 500(1.03045453395)
Finally, multiply by the principal amount:
A = $515.23
So, Max and Danielle will have $515.23 to spend on their trip in 3 years.
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