Annuities, EMI, Sinking Fund and Depreciation Calculations Questions

Question 1

Define annuity.

Accepted Answer

An annuity is a series of equal payments or receipts made at equal time intervals.

Question 2

What is an ordinary annuity?

Accepted Answer

An ordinary annuity is an annuity in which payments are made at the end of each period.

Question 3

Define annuity due.

Accepted Answer

An annuity due is an annuity in which payments are made at the beginning of each period.

Question 4

What is EMI?

Accepted Answer

EMI is the equated monthly instalment paid every month to repay a loan with interest.

Question 5

What is a sinking fund?

Accepted Answer

A sinking fund is a plan of equal periodic deposits to accumulate a future sum for a specific purpose.

Question 6

State one method of depreciation.

Accepted Answer

Straight line method (SLM) is one method of depreciation.

Question 7

Differentiate between ordinary annuity and annuity due (any three points).

Accepted Answer

Ordinary annuity: payments occur at the end of each period; annuity due: payments occur at the beginning.

Annuity due gives one extra period of interest on each payment, so its PV and FV are higher than ordinary annuity.

Examples: Ordinary—loan instalment at month end; Due—rent paid at start of month.

Question 8

Calculate FV of ordinary annuity: deposit ₹2,000 per year for 3 years at 10% p.a. (end of year).

Accepted Answer

R = 2,000, i = 0.10, n = 3.
FV = R × [((1+i)^n − 1)/i]
= 2,000 × [((1.10)^3 − 1)/0.10]
(1.10)^3 = 1.331
Factor = (1.331 − 1)/0.10 = 3.31
FV = 2,000 × 3.31 = ₹6,620 (approx).

Question 9

Find PV of ordinary annuity: ₹5,000 per year for 2 years at 10% p.a.

Accepted Answer

R = 5,000, i = 0.10, n = 2.
PV = R × [1 − 1/(1+i)^n] / i
= 5,000 × [1 − 1/(1.10)^2] / 0.10
(1.10)^2 = 1.21 so 1/1.21 ≈ 0.82645
Bracket = 1 − 0.82645 = 0.17355
PV = 5,000 × (0.17355/0.10) = 5,000 × 1.7355 ≈ ₹8,678 (approx).

Question 10

Explain why EMI interest part decreases over time.

Accepted Answer

EMI is calculated on the outstanding loan balance. At the start, outstanding principal is high, so interest is high.

Every EMI repays some principal, reducing outstanding balance. Therefore interest (rate × balance) decreases over time and principal component increases.

Question 11

Compute depreciation per year under SLM: Cost ₹1,00,000, scrap ₹10,000, life 5 years.

Accepted Answer

Depreciation per year = (Cost − Scrap)/Life = (1,00,000 − 10,000)/5 = 90,000/5 = ₹18,000.

Question 12

Find book value after 2 years under WDV: Cost ₹50,000, depreciation rate 10% p.a.

Accepted Answer

BV after n years = Cost × (1 − r)^n = 50,000 × (0.90)^2 = 50,000 × 0.81 = ₹40,500.

Question 13

Explain sinking fund and show how to find periodic deposit needed to accumulate a future sum. Give an example.

Accepted Answer

A sinking fund is a method of accumulating a target amount by making equal periodic deposits that earn interest. It is commonly used for replacement of assets or repayment of loans/debentures.

If deposit each period is R, rate per period is i, and number of periods is n, the accumulated amount is:
S = R × [((1+i)^n − 1)/i]
So required deposit:
R = S / [((1+i)^n − 1)/i]

Example: To accumulate ₹1,00,000 in 5 years at 10% p.a. with annual deposits:
Factor = ((1.10)^5 − 1)/0.10 = (1.61051 − 1)/0.10 = 6.1051
R = 1,00,000/6.1051 ≈ ₹16,380 (approx).

Thus, equal deposits plus interest create the future fund.

Question 14

Explain EMI and loan amortization with an example.

Accepted Answer

EMI (Equated Monthly Instalment) is a fixed monthly payment to repay a loan. Each EMI contains:
1) interest on outstanding principal, and
2) principal repayment.

In the beginning, outstanding principal is high, so interest is high and principal repaid is low. As principal reduces, interest decreases and principal component increases. This process is called amortization.

Example (illustrative): Loan balance ₹1,00,000, monthly rate 1%, EMI ₹4,500.
Interest for month 1 = 1% of 1,00,000 = ₹1,000
Principal repaid = 4,500 − 1,000 = ₹3,500
New balance = 1,00,000 − 3,500 = ₹96,500
Next month interest is 1% of 96,500 = ₹965 (lower).

Hence, EMI stays constant but its components change over time.

Question 15

Compare SLM and WDV methods of depreciation with merits and suitable situations.

Accepted Answer

Straight Line Method (SLM)
- Depreciation is equal each year: (Cost − Scrap)/Life.
- Book value reduces uniformly.
- Suitable when asset gives uniform benefit and repairs are stable.
- Simple and easy for budgeting.

Written Down Value (WDV)
- Depreciation is charged on reducing book value: BV after n years = Cost × (1 − r)^n.
- Higher depreciation in early years, lower in later years.
- Suitable when asset is more productive initially or becomes obsolete quickly.

Merits/Conclusion:
SLM gives stable annual expense and stable profit impact. WDV matches higher early usage/obsolescence and is common in practice/tax contexts. Choose based on usage pattern.

Annuities, EMI, Sinking Fund and Depreciation Calculations

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