Question
Rick put his $200 into a simple interest account at 3.25% interest. Julian put his $200 into a compound interest account that gives 3% interest compounded annually. The table below shows their yearly balance after interest has been applied.
Balance
Rick
Julian
deposit
200
200
Year 1
206.50
206.00
Year 2
213.00
212.18
Year 3
219.50
218.55
Year 4
226.00
225.11
Year 5
232.50
231.85
Year 6
239.00
238.81
Year 7
245.50
245.97
Year 8
252.00
253.35
Year 9
258.50
260.95
Year 10
265.00
268.78
Which statements are true about their balances? Select four options.
After 10 years, Rick has a larger balance than Julian.
Julian accumulated $3.78 more in interest after 10 years.
Julian’s bank pays greater interest if he keeps his money in the bank for more than seven years.
Julian’s balance increases by the same amount each year.
Julian’s bank pays greater interest if he keeps his money in the bank for less than seven years.
Rick’s balance increases by the same amount each year.
After five years, Rick has a larger balance than Julian.
Julian accumulated $0.65 more interest after five years.
Balance
Rick
Julian
deposit
200
200
Year 1
206.50
206.00
Year 2
213.00
212.18
Year 3
219.50
218.55
Year 4
226.00
225.11
Year 5
232.50
231.85
Year 6
239.00
238.81
Year 7
245.50
245.97
Year 8
252.00
253.35
Year 9
258.50
260.95
Year 10
265.00
268.78
Which statements are true about their balances? Select four options.
After 10 years, Rick has a larger balance than Julian.
Julian accumulated $3.78 more in interest after 10 years.
Julian’s bank pays greater interest if he keeps his money in the bank for more than seven years.
Julian’s balance increases by the same amount each year.
Julian’s bank pays greater interest if he keeps his money in the bank for less than seven years.
Rick’s balance increases by the same amount each year.
After five years, Rick has a larger balance than Julian.
Julian accumulated $0.65 more interest after five years.
Answers
GPT-4o mini
Let's evaluate each statement one by one based on the provided figures for Rick's and Julian's savings accounts after 10 years.
1. **After 10 years, Rick has a larger balance than Julian.**
- Rick's balance after 10 years: $265.00
- Julian's balance after 10 years: $268.78
- **This statement is false.**
2. **Julian accumulated $3.78 more in interest after 10 years.**
- Interest earned by Rick in 10 years: $265.00 - $200.00 = $65.00
- Interest earned by Julian in 10 years: $268.78 - $200.00 = $68.78
- Difference in interest: $68.78 - $65.00 = $3.78
- **This statement is true.**
3. **Julian’s bank pays greater interest if he keeps his money in the bank for more than seven years.**
- We have to compare the total interest earned after 7 years.
- Interest earned by Rick in 7 years: $245.50 - $200.00 = $45.50
- Interest earned by Julian in 7 years: $245.97 - $200.00 = $45.97
- Julian’s interest is greater at 7 years but not after 5 years, so this statement doesn't imply a clear comparison past 7 years without specific values.
- **This statement is ambiguous or potentially false.**
4. **Julian’s balance increases by the same amount each year.**
- Julian's balances for each year: 206.00, 212.18, 218.55, 225.11, 231.85, 238.81, 245.97, 253.35, 260.95, 268.78 (increases are not consistent).
- **This statement is false.**
5. **Julian’s bank pays greater interest if he keeps his money in the bank for less than seven years.**
- This is a comparative statement, as calculated above, we see that Julian has not less the entire time up to 7 years. Thus, it holds true up to that period.
- **Ambiguous unless more details were given so this may be false.**
6. **Rick’s balance increases by the same amount each year.**
- Rick's increase is consistent: $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50 each year.
- **This statement is true.**
7. **After five years, Rick has a larger balance than Julian.**
- Rick's balance after 5 years: $232.50
- Julian's balance after 5 years: $231.85
- **This statement is true.**
8. **Julian accumulated $0.65 more interest after five years.**
- Interest earned by Rick in 5 years: $232.50 - $200.00 = $32.50
- Interest earned by Julian in 5 years: $231.85 - $200.00 = $31.85
- Difference in interest: $32.50 - $31.85 = $0.65
- **This statement is true.**
In conclusion, the four true statements are:
1. Julian accumulated $3.78 more in interest after 10 years.
2. Rick’s balance increases by the same amount each year.
3. After five years, Rick has a larger balance than Julian.
4. Julian accumulated $0.65 more interest after five years.
1. **After 10 years, Rick has a larger balance than Julian.**
- Rick's balance after 10 years: $265.00
- Julian's balance after 10 years: $268.78
- **This statement is false.**
2. **Julian accumulated $3.78 more in interest after 10 years.**
- Interest earned by Rick in 10 years: $265.00 - $200.00 = $65.00
- Interest earned by Julian in 10 years: $268.78 - $200.00 = $68.78
- Difference in interest: $68.78 - $65.00 = $3.78
- **This statement is true.**
3. **Julian’s bank pays greater interest if he keeps his money in the bank for more than seven years.**
- We have to compare the total interest earned after 7 years.
- Interest earned by Rick in 7 years: $245.50 - $200.00 = $45.50
- Interest earned by Julian in 7 years: $245.97 - $200.00 = $45.97
- Julian’s interest is greater at 7 years but not after 5 years, so this statement doesn't imply a clear comparison past 7 years without specific values.
- **This statement is ambiguous or potentially false.**
4. **Julian’s balance increases by the same amount each year.**
- Julian's balances for each year: 206.00, 212.18, 218.55, 225.11, 231.85, 238.81, 245.97, 253.35, 260.95, 268.78 (increases are not consistent).
- **This statement is false.**
5. **Julian’s bank pays greater interest if he keeps his money in the bank for less than seven years.**
- This is a comparative statement, as calculated above, we see that Julian has not less the entire time up to 7 years. Thus, it holds true up to that period.
- **Ambiguous unless more details were given so this may be false.**
6. **Rick’s balance increases by the same amount each year.**
- Rick's increase is consistent: $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50, $6.50 each year.
- **This statement is true.**
7. **After five years, Rick has a larger balance than Julian.**
- Rick's balance after 5 years: $232.50
- Julian's balance after 5 years: $231.85
- **This statement is true.**
8. **Julian accumulated $0.65 more interest after five years.**
- Interest earned by Rick in 5 years: $232.50 - $200.00 = $32.50
- Interest earned by Julian in 5 years: $231.85 - $200.00 = $31.85
- Difference in interest: $32.50 - $31.85 = $0.65
- **This statement is true.**
In conclusion, the four true statements are:
1. Julian accumulated $3.78 more in interest after 10 years.
2. Rick’s balance increases by the same amount each year.
3. After five years, Rick has a larger balance than Julian.
4. Julian accumulated $0.65 more interest after five years.