a) The compound interest formula is, in general,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where P is the initial amount, r is the interest rate, and n is the number of times the interest is compounded per unit t.
In our case,
[tex]A=150000,n=12,r=0.105(=10.5\%),t=4[/tex]
Thus, solving for P,
[tex]\begin{gathered} \Rightarrow P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ \Rightarrow P=\frac{150000}{(1+\frac{0.105}{12})^{12\cdot4}} \\ \Rightarrow P=98737.2365\ldots \end{gathered}[/tex]
The answer to part a) is approximately $98737.24-> Interest + initial inversion equal to $150000
b)
We need to subtract P from Clem's inheritance, as shown below.
[tex]250000-P\approx151262.76[/tex]
The answer to part b) is approximately $151262.76.
c)
Set P=250000 and solve for A as shown below.
[tex]\begin{gathered} P=250000 \\ \Rightarrow A=250000(1+\frac{0.105}{12})^{12\cdot4} \\ \Rightarrow A=379795.924153\ldots \\ \Rightarrow A\approx379795.92 \\ \text{and} \\ I=A-P=379795.92-250000=129795.92\to\text{interest} \end{gathered}[/tex]
The answer to part c) is $129795.92-> Only interest
