Becky invested $19,800 in a CD that pays an annual interest rate of 5.3%. The CD is set to compound daily (365 times per year). How much is in Becky’s account after 9 years?
a:$12,807.53
b:$31,901.31
c:$12,957.19
d:$19,777.01
To calculate how much money is in Becky's account after 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the given values:
A = 19800(1 + 0.053/365)^(365*9)
Calculating within the parentheses:
A = 19800(1.000145205479452)^3285
Calculating the exponent:
A ≈ 19800(3.183098591)
A ≈ 63142.372
Therefore, the answer is b:$31,901.31.