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?
To calculate the amount in Becky's account after 9 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Becky invested $19,800 at an annual interest rate of 5.3% (or 0.053), with daily compounding (n = 365 times per year), and for a period of 9 years (t = 9).
Plugging in the values into the formula:
A = 19800(1 + 0.053/365)^(365*9)
Simplifying the equation inside the parentheses:
A = 19800(1 + 0.0001452)^(365*9)
Calculating the exponent:
A = 19800(1.0001452)^(3285)
Calculating the final result:
A ≈ 19800 * 1.657696
A ≈ $32,762.93
Therefore, after 9 years, the amount in Becky's account will be approximately $32,762.93.