Answer: Sussy initially deposited $31.61.
Step-by-step explanation: 5% interest rate for 6 months with $32.45 earned, we can use the compound interest formula A=P(1 + r/n)^nt where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year and t is the time in years.
In this case, we know that P is what we are looking for, r=5%, n=2 (since it’s compounded twice a year), t=6/12=0.5 years and A=P+$32.45.
Substituting these values into the formula gives us:
A=P(1 + r/n)^nt + $32.45
$32.45=P(1 + 0.05/2)^(2*0.5)
$32.45=P(1 + 0.025)^1
$32.45=P(1.025)
P=$31.61