Answer
${{\$}} 1021.60$
Work Step by Step
The amount A after t years due to a principal P
invested at an annual interest rate r, expressed as a decimal,
compounded n times per year is $A=P\displaystyle \cdot(1+\frac{r}{n})^{nt}$
If compounding is continuous, $A=Pe^{rt}$
---
t = 3 months = $0.25$ years,
$r=0.068$
On April 1, Kim will have (continuous compunding):
$A=1000e^{(0.068)(0.25)}={{\$}} 1017.15$
Now, $P=1017.15$,
the compounding is $n=12$ times per year,
$r=0.0525,$
$t=$ 1 month = $\displaystyle \frac{1}{12}$ years.
The amount on May 1:
$A=1017.15\displaystyle \left(1+\frac{0.0525}{12}\right)^{(12)(1/12)}={{\$}} 1021.60$
