Hey all, hoping someone can shed some light on Greg’s solution to question 13 on the second Algebra Foundation Quiz.
In Greg’s solution, he calculates the amount for the compounded account as: 100(1.03)^4. He has divided the amount of years into 4, which makes sense because the compounding occurs twice a year for 2 years. However, he’s only halved the rate (i.e. interest rate given in problem = 6% so Greg’s taken .06/2 = .03).
Why wouldn’t the rate be divided by 4 to align with the number of “mini-years” that the account undergoes? When I solved this problem, I divided the rate by 4 (i.e. .06/4 = .015).
You want the rate per year
That doesn’t answer my question. Why would we not divide the rate into the number of mini years (like we do with the time value)?
Why should we divide by 4? That doesn’t make much sense.
If the annual interest rate is 6\% then the interest rate for compounding semi-annually would be approximately \frac 62 \% = 3\% (there’s some overshooting here but this is convention so we go with that).
100 → 1st compounding → 2nd compounding → 3rd compounding → 4th compounding
After the first compounding, you have 100(1.03)^1 and then if you repeat it three more times, you have 100(1.03)^4. For each compounding, we’re just increasing our principal by 3\% because that’s what we expect to obtain (approximately) every 6 months.
I rewatched the Prepswift video on this, and I understand now. Essentially we’re always just dividing the given interest rate by the number of mini-years in one year, rather than the total number of mini-years given in the question. Thank you for your help.