Find the amount of compound interest earned in an account that opens with $24,000, earns 3.5% interest compounded daily, and is held for 10 years. Assume 360 days in a year. (Round your answer to the nearest cent.)
$
i = .035/360 = .000097222
n = 10*360 = 3600
amount = 24000(1.000097222)^3600
= 34057.04
so the interest earned = 34057.04-24000 = 10057.04
To find the amount of compound interest earned in this scenario, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
where:
A = the final amount of money,
P = the principal amount (initial investment),
r = annual interest rate (in decimal form),
n = number of times interest is compounded per year, and
t = number of years.
In this case,
P = $24,000,
r = 3.5% = 0.035,
n = 365 (since interest is compounded daily),
and t = 10.
Plugging the values into the formula:
A = 24000 * (1 + 0.035/365)^(365*10) - 24000
Let's calculate it step by step:
1. First, calculate the value inside the parentheses:
(1 + 0.035/365) = 1.0000958904109589
2. Then, calculate the exponent:
365 * 10 = 3650
3. Next, raise the value inside the parentheses to the exponent:
(1.0000958904109589)^(3650) = 1.41743927131
4. Finally, plug this value back into the original formula to get the final amount (A):
A = 24000 * 1.41743927131 - 24000
A = $34,737.43
To find the amount of compound interest earned, we subtract the principal amount (P) from the final amount (A):
Compound Interest = A - P
Compound Interest = $34,737.43 - $24,000
Therefore, the amount of compound interest earned is $10,737.43.