Question

If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45-day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3? Round to the nearest penny.

Answer 1

I don’t have the emergency-fund amount (or the monthly amount) or the text of question #3, so I can’t give a single dollar answer yet. I can give the formula and an example — or compute it if you tell me the emergency-fund total or the 1‑month dollar amount.

Let:
- E = total emergency fund
- M = 1 month’s worth (so M = E/N if the fund is N months)
- r_sav = 0.0315 (3.15% APR)
- r_cd = 0.0465 (4.65% APR)
- t = 45/365 (fraction of year)

If question #3 was the case where the entire fund E was in the savings account, the 45‑day interest difference when you move (E − M) into the 45‑day CD is

Difference = (E − M) * (r_cd − r_sav) * (45/365).

If the emergency fund is N months and M is one month, E − M = (N − 1)M, so

Difference = (N − 1) * M * (r_cd − r_sav) * (45/365).

Numerical example (common assumption: a 6‑month emergency fund, so N = 6):
Difference = 5 * M * (0.0465 − 0.0315) * (45/365)
= 5 * M * 0.015 * 0.123287671
≈ 0.009246575 * M.

So per $1,000 of one month’s expenses (M = $1,000) the extra interest in 45 days is about $9.25. Example totals:
- If M = $2,000 (so 6‑month fund = $12,000): difference ≈ $18.49
- If M = $3,000: difference ≈ $27.74

Tell me the monthly amount (or the total emergency fund and how many months it represents) and I’ll compute the rounded difference to the nearest penny.