Rayden invested $20 000 at a rate of 0.3% per month compound interest.

1. Convert the time and monthly percentage rate for use in the compound interest formula.

$2$ years $= 24$ months

$0.3\% = \dfrac{0.3}{100} = 0.003$

Monthly multiplier $= 1 + 0.003 = 1.003$

2. Apply the compound interest formula and round the money value appropriately.

$\text{Value} = 20000(1.003)^{24}$

$= 21490.784\ldots$

$\approx 21490.78$

1. Form an equation comparing the remaining investment to the required final value.

After withdrawing $\dfrac15$ of the accumulated amount, the remaining amount is
$\dfrac45 \times \text{amount in (a)}.$
Let the new monthly interest rate be $r\%$.

Over another 3 years, there are $36$ months, so
$\dfrac45 A\left(1+\dfrac{r}{100}\right)^{36}=A,$
where $A$ is the value found in part (a).

2. Solve for the new monthly compound interest rate.

Cancel $A$ from both sides:
$\dfrac45\left(1+\dfrac{r}{100}\right)^{36}=1$
$\left(1+\dfrac{r}{100}\right)^{36}=\dfrac54$
$1+\dfrac{r}{100}=\left(\dfrac54\right)^{\frac1{36}}$
$r=100\left[\left(\dfrac54\right)^{\frac1{36}}-1\right]$
$r=0.6217\ldots$
Hence the new rate is $0.622\%$ per month, to 3 significant figures.