Question

compare simple and compound
ms. tamney and mrs. enderle each deposit $5000 into accounts that
earn 5% interest. ms. tamney’s account earns simple interest while mrs.
enderle’s account earns annual compound interest. the table below
shows how much interest is earned each year for the first 3 years in
each account.
tamney
calculation
year 1
5,000(0.05)
year 2
5,000(0.05)
year 3
5,000(0.05)
interest
$250
$250
$250
total interest earned:
$750
who will earn more interest after
three years, and how much
more?
using the tables, describe any
differences between ms. tamney
and mrs. enderle’s interest
calculations.

Explanation:

Step1: Calculate Ms. Tamney's total interest

Ms. Tamney earns simple interest. The formula for simple interest is $I = P \times r \times t$, where $P = 5000$, $r = 0.05$, $t = 3$. So $I = 5000 \times 0.05 \times 3 = 750$.

Step2: Calculate Mrs. Enderle's total interest

From the table, Mrs. Enderle's interest for Year 1: $250$, Year 2: $250$, Year 3: $250$? Wait, no, wait. Wait, compound interest: Year 1 interest is $5000 \times 0.05 = 250$, so principal for Year 2 is $5000 + 250 = 5250$. Then Year 2 interest is $5250 \times 0.05 = 262.5$, Year 3 interest is $(5250 + 262.5) \times 0.05 = 5512.5 \times 0.05 = 275.625$. Wait, but the table shows Year 1: $250$, Year 2: $250$, Year 3: $250$? Wait, no, maybe the table is wrong? Wait, no, the table given for Tamney (wait, no, the table is for Tamney? Wait, the table says "Tamney" with calculation $5000(0.05)$ each year, interest $250$ each year, total interest $750$. Wait, maybe Mrs. Enderle's compound interest: Wait, no, the problem says "Ms. Tamney’s account earns simple interest while Mrs. Enderle’s account earns annual compound interest". Wait, the table provided is for Tamney? Wait, the table has "Tamney" with Year 1: $5000(0.05)$ interest $250$, Year 2: $5000(0.05)$ interest $250$, Year 3: $5000(0.05)$ interest $250$, total interest $750$. But that's simple interest. Wait, maybe the table is mislabeled? Wait, no, the problem says "the table below shows how much interest is earned each year for the first 3 years in each account". So Tamney's account (simple interest) has interest $250$ each year, total $750$. Now Mrs. Enderle's compound interest: Year 1: $5000 \times 0.05 = 250$, principal becomes $5000 + 250 = 5250$. Year 2: $5250 \times 0.05 = 262.5$, principal becomes $5250 + 262.5 = 5512.5$. Year 3: $5512.5 \times 0.05 = 275.625$. So total compound interest: $250 + 262.5 + 275.625 = 788.125$. Wait, but the table for Tamney (simple) has total $750$. Wait, no, maybe the table is for Mrs. Enderle? Wait, the problem says "Ms. Tamney’s account earns simple interest while Mrs. Enderle’s account earns annual compound interest. The table below shows how much interest is earned each year for the first 3 years in each account." Wait, the table is labeled "Tamney" with calculation $5000(0.05)$ each year, interest $250$ each year, total $750$. So that's simple interest (Tamney). Now Mrs. Enderle's compound interest: Let's recalculate. Year 1: $I_1 = 5000 \times 0.05 = 250$, $A_1 = 5000 + 250 = 5250$. Year 2: $I_2 = 5250 \times 0.05 = 262.5$, $A_2 = 5250 + 262.5 = 5512.5$. Year 3: $I_3 = 5512.5 \times 0.05 = 275.625$, $A_3 = 5512.5 + 275.625 = 5788.125$. Total compound interest: $250 + 262.5 + 275.625 = 788.125$. Tamney's total interest: $5000 \times 0.05 \times 3 = 750$. So Mrs. Enderle earns more. The difference is $788.125 - 750 = 38.125$. Wait, but maybe the table for Mrs. Enderle is different? Wait, the table given is for Tamney (simple), so we need to calculate compound for Enderle.

Step3: Compare total interests

Tamney's total interest: $750$. Enderle's total interest: $250 + 262.5 + 275.625 = 788.125$. Difference: $788.125 - 750 = 38.125$. So Mrs. Enderle earns more, by $38.125$ (or $38.13$ if rounded).

Answer:

Mrs. Enderle will earn more interest. The total interest for Ms. Tamney (simple) is $750$, and for Mrs. Enderle (compound) is $788.125$ (or calculated as above). The difference is $38.125$ (or $38.13$). So Mrs. Enderle earns $38.125$ more than Ms. Tamney after three years.