Answer:
Therefore the bank need to offer 23.6% annual interest rate compounded twice.
Step-by-step explanation:
Compound interest formula:
[tex]A=P(1+\frac rn)^{nt}[/tex]
A=Amount
P=Principal
r=rate of interest
n= Number of times interest is compounded per year.
t= time
Bank A
P=$55,000, r=25% = 0.25, n=1, t=t
The amount that the school have to pay after t year is
[tex]A_1=55,000(1+0.25)^t[/tex]
[tex]=55000(1.25)^t[/tex]
Bank B
P=$55,000, r=?, n=2, t=t
The amount that the school have to pay after t year is
[tex]A_2=55,000(1+\frac r2)^{2t}[/tex]
Since the amount for both banks are same.
i.e
[tex]A_1=A_2[/tex]
[tex]\Rightarrow 55000(1.25)^t=55000(1+\frac r2)^{2t}[/tex]
[tex]\Rightarrow (1.25)^t=(1+\frac r2)^{2t}[/tex]
[tex]\Rightarrow (1.25)=(1+\frac r2)^{2}[/tex]
[tex]\Rightarrow (1+\frac r2)=\sqrt{1.25}[/tex]
[tex]\Rightarrow (1+\frac r2)=1.118[/tex]
[tex]\Rightarrow \frac r2=1.118-1[/tex]
[tex]\Rightarrow \frac r2=0.118[/tex]
⇒r=0.118×2
⇒r = 0.236
⇒r =23.6%
Therefore the bank need to offer 23.6% annual interest rate compounded twice.
