Question

Paddy and Anna each invest $2000 for 5 years.

Answer 1

Answer: r= 1.22

Step-by-step explanation:

Formula for amount with simple interest = $P(1+rt)$

, where

P= principal value , r= rate of interest , t = time.

Given: P=  $2000, t= 5 years, r= 1.25% = 0.0125

$A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125$

Formula to compute compound amount : $P(1+r)^t$

$=2000(1+r)^5$

When both have same worth then

$2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625$

taking log on both sides , we get

$5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%$

Hence, Value of r= 1.22