Beginning-of-year versus end-of-year deposits
Series X-A case study · set 2, case 2 of 9 · 5 questions · 1 mark each
Question 1 of 5Case practice
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Two siblings each plan to save ₹20,000 a year for three years in an account earning 10% annually. Saira deposits at the beginning of each year, at times 0, 1 and 2. Omar deposits at the end of each year, at times 1, 2 and 3. Both accounts are measured immediately after time 3. Each makes exactly three deposits and neither withdraws money. There are no fees, taxes or different interest rates. Their discussion is only about the effect of payment timing. Neither plan is a promise about real investment returns. Use annual compounding and keep all cash-flow dates explicit.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
Two siblings each plan to save ₹20,000 a year for three years in an account earning 10% annually. Saira deposits at the beginning of each year, at times 0, 1 and 2. Omar deposits at the end of each year, at times 1, 2 and 3. Both accounts are measured immediately after time 3. Each makes exactly three deposits and neither withdraws money. There are no fees, taxes or different interest rates. Their discussion is only about the effect of payment timing. Neither plan is a promise about real investment returns. Use annual compounding and keep all cash-flow dates explicit.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What is Saira’s account value at time 3?
Option A. ₹66,200
Why it is wrong: This is the value of Omar’s end-of-year plan.
Option B. ₹72,820 — Correct answer
Option C. ₹79,420
Why it is wrong: This gives one deposit an extra period not in the schedule.
Option D. ₹60,000
Why it is wrong: This ignores interest.
Answer: B. ₹20,000 × (1.10³ + 1.10² + 1.10) = ₹72,820. Remember: An annuity due starts each contribution one period earlier.
Hint, shown before you answer in practice mode: Her three deposits grow for three, two and one years.
XA-S2-C02-Q1mediumnumerical
Q2What is Omar’s account value at time 3?
Option A. ₹60,000
Why it is wrong: This ignores interest.
Option B. ₹72,820
Why it is wrong: This gives every deposit one additional year.
Option C. ₹66,200 — Correct answer
Option D. ₹64,000
Why it is wrong: This omits compounding on the first deposit.
Answer: C. ₹20,000 × (1.10² + 1.10 + 1) = ₹66,200. Remember: The final ordinary-annuity payment earns no interest before its measurement date.
Hint, shown before you answer in practice mode: His deposits grow for two, one and zero years.
XA-S2-C02-Q2mediumnumerical
Q3How much additional value does Saira’s earlier timing produce?
Option A. ₹12,820
Why it is wrong: This is Saira’s total interest, not the difference.
Option B. ₹20,000
Why it is wrong: Both siblings contribute the same total principal.
Option C. ₹2,000
Why it is wrong: This counts one deposit’s extra interest only.
Option D. ₹6,620 — Correct answer
Answer: D. ₹72,820 − ₹66,200 = ₹6,620. This also equals 10% of ₹66,200. Remember: Earlier cash flows can add value without increasing total contributions.
Hint, shown before you answer in practice mode: Subtract the two future values.
XA-S2-C02-Q3mediumnumerical
Q4How much of Saira’s time-3 value is interest?
Option A. ₹6,200
Why it is wrong: This is Omar’s total interest.
Option B. ₹72,820
Why it is wrong: This includes contributions as well as interest.
Option C. ₹12,820 — Correct answer
Option D. ₹6,620
Why it is wrong: This is the advantage over Omar’s plan.
Answer: C. ₹72,820 − 3 × ₹20,000 = ₹12,820. Remember: Investment gain is ending value less the principal contributed, when there are no withdrawals.
Hint, shown before you answer in practice mode: Subtract her three deposits from the account value.
XA-S2-C02-Q4mediumnumerical
Q5Which statement explains the difference between their accounts?
Option A. Saira contributes more principal.
Why it is wrong: Both contribute three amounts of ₹20,000.
Option B. Each of Saira’s deposits earns interest for one more year than the matching Omar deposit. — Correct answer
Option C. Saira makes a fourth deposit at time 3.
Why it is wrong: Her deposits occur only at times 0, 1 and 2.
Option D. Omar’s rate is lower.
Why it is wrong: Both receive the same assumed 10% rate.
Answer: B. Moving each deposit one year earlier multiplies its ending value by 1.10. The number and size of deposits are unchanged. Remember: Payment timing is a separate variable from payment amount and return.
Hint, shown before you answer in practice mode: Compare matching deposits, not just the final balances.
XA-S2-C02-Q5mediumapplication
A cheaper loan rate with a refinancing fee
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