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.

Answer 1

The four true statements are:

- Julian accumulated $3.78 more in interest after 10 years. (268.78 − 200 = 68.78 vs Rick 265 − 200 = 65.00; difference = 3.78.)
- Julian’s bank pays greater interest if he keeps his money in the bank for more than seven years. (Julian’s balance exceeds Rick’s starting at year 8.)
- Rick’s balance increases by the same amount each year. (Simple interest gives a constant $200 × 0.0325 = $6.50 per year.)
- After five years, Rick has a larger balance than Julian. (232.50 vs 231.85.)