1. If interest is compounded quarterly, the "Effective Annual Rate" (EAR) will be:
Half of the Nominal Rate.
Lower than the Nominal Rate.
Equal to the Nominal Rate.
Higher than the Nominal Rate.
Explanation:
When compounding occurs more frequently than once a year (e.g., quarterly), interest is earned on interest more often, making the Effective Annual Rate (EAR) higher than the stated Nominal Rate.
2. According to the "Rule of 72", if the interest rate is 8% p.a., an investment will double in approximately:
9 years
10 years
8 years
5 years
Explanation:
Rule of 72 formula: Years to Double ˜ 72 / Interest Rate. Here, 72 / 8 = 9 years.
3. A "Perpetuity" is an annuity that:
Ends after 10 years.
Has uneven cash flows.
Continues forever (infinite life).
Pays interest at the beginning of the period.
Explanation:
Perpetuity is a stream of constant cash flows that continues indefinitely. PV of Perpetuity = Annual Cash Flow / Discount Rate.
4. An "Annuity Due" differs from an "Ordinary Annuity" in that payments are made:
Irregularly.
Only once.
At the beginning of each period.
At the end of each period.
Explanation:
In an Ordinary Annuity, cash flows occur at the end of the period (e.g., bond interest). In Annuity Due, cash flows occur at the beginning (e.g., rent, insurance premium).
5. A Sinking Fund factor is used to calculate:
The amount of annuity required to accumulate a specific future sum.
The compound interest.
The future value of a single amount.
The present value of a perpetuity.
Explanation:
If you need ?10 Lakhs after 5 years to repay a bond, the Sinking Fund factor helps you calculate how much you need to save annually to reach that target.
6. For a given nominal interest rate and time period, the Future Value will be highest if compounding is done:
Semi-annually.
Daily.
Quarterly.
Annually.
Explanation:
More frequent compounding results in interest being earned on interest sooner, leading to a higher final amount. Daily > Quarterly > Annual.
7. As the discount rate (interest rate) increases, the Present Value of a future sum will:
Decrease.
Become negative.
Increase.
Remain same.
Explanation:
There is an inverse relationship. A higher discount rate means money loses value faster over time, so the current worth of a future sum is lower.
8. Calculate the Effective Annual Rate (EAR) if the nominal rate is 12% compounded monthly.
Explanation:
Formula: EAR = (1 + r/n)^n - 1. Here r=0.12, n=12. EAR = (1 + 0.01)^12 - 1 = 1.1268 - 1 = 0.1268 or 12.68%.
9. Which formula represents the Present Value (PV) of a single future sum?
PV = FV / (1+r)^n
PV = FV * n * r
PV = FV * (1+r)^n
PV = FV / r
Explanation:
To find the present value, we divide the future value by the compounding factor (1+r)^n.
10. Using the "Rule of 69", if the interest rate is 10%, the doubling period is approximately:
6.9 years
10 years
6.9 years + 0.35
7.25 years
Explanation:
Rule of 69 Formula: Doubling Period = 0.35 + (69 / Interest Rate). Here, 0.35 + (69/10) = 0.35 + 6.9 = 7.25 years. This is more accurate for continuous compounding.
11. Which factor would you use to calculate the monthly EMI for a Housing Loan?
Future Value Interest Factor of an Annuity (FVIFA).
Present Value Interest Factor of an Annuity (PVIFA).
Future Value Interest Factor of a Lump Sum (FVIF).
Present Value Interest Factor of a Lump Sum (PVIF).
Explanation:
A loan is a lump sum received today (PV), which is repaid in installments (Annuity). To equate the loan amount to the stream of EMIs, we use PVIFA.
12. In a loan amortization schedule with constant EMI, as time passes:
Both components remain constant.
The interest component increases, and principal component decreases.
The interest component decreases, and principal component increases.
The EMI amount increases.
Explanation:
In the early years, the outstanding principal is high, so interest is high. As principal is repaid, interest drops, allowing a larger portion of the fixed EMI to go towards principal repayment.
13. To calculate the accumulated value of a systematic investment plan (SIP) at the end of the tenure, you would use the formula for:
Future Value of an Annuity.
Present Value of an Annuity.
Future Value of a Single Amount.
Perpetuity.
Explanation:
SIP involves a series of equal payments at regular intervals. We want to know the total value at the end (Future), so FV of Annuity is used.
14. The exact Fisher Equation relating Nominal Rate (r), Real Rate (R), and Inflation (i) is:
r = R + i
r = R * i
R = r - i
(1 + r) = (1 + R) * (1 + i)
Explanation:
While r = R + i is a common approximation, the precise relationship accounts for the cross-product of real rate and inflation: r = R + i + (R*i). Thus, (1+r) is the product of (1+R) and (1+i).
15. A "Deferred Annuity" is one where:
Payments are made at the beginning of each period.
Payments start immediately.
Payments continue forever.
The first payment is delayed for a certain number of periods.
Explanation:
Example: A pension plan where you invest now, but the annuity payments (pension) start only after you retire (say, after 10 years).
16. The Present Value of a perpetuity that grows at a constant rate 'g' is calculated as:
Cash Flow / (Discount Rate + Growth Rate)
Cash Flow / Discount Rate
Cash Flow / (Discount Rate - Growth Rate)
Cash Flow * Growth Rate
Explanation:
Formula: PV = CF1 / (k - g). This is used when cash flows grow forever at a constant rate (e.g., valuation of a stock with constant dividend growth).