Can Someone Please Explain?

Question

Winston deposits $10 into a fund today and $20 fifteen years later. Interested is credited at a nominal discount rate of 𝑑 compounded quarterly for the first 10 years, and a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is $100. Find 𝑑.

I know it will be 10(1-d/4)^(-4*10) which we can call k

And then k(1.03)^(20*2)... I jus want to know the reasoning as to why it would be raised to 2*20 and not 2*5. Can someone please explain?

Answer 1

I hope this helps!