Answer: r= 1.22
Step-by-step explanation:
Formula for amount with simple interest = [tex]P(1+rt)[/tex]
, where
P= principal value , r= rate of interest , t = time.
Given: P= $2000, t= 5 years, r= 1.25% = 0.0125
[tex]A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125[/tex]
Formula to compute compound amount : [tex]P(1+r)^t[/tex]
[tex]=2000(1+r)^5[/tex]
When both have same worth then
[tex]2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625[/tex]
taking log on both sides , we get
[tex]5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%[/tex]
Hence, Value of r= 1.22
