Simple and Compound Interest; Present Value and Future Value Questions

Question 1

Define simple interest.

Accepted Answer

Simple interest is interest calculated only on the original principal for the entire period.

Question 2

Write the formula of simple interest.

Accepted Answer

I = (P × R × T) / 100.

Question 3

What is compound interest?

Accepted Answer

Compound interest is interest calculated on principal plus accumulated interest.

Question 4

Write the formula for amount under compound interest (annual).

Accepted Answer

A = P (1 + R/100)^T.

Question 5

Define present value (PV).

Accepted Answer

Present value is today’s value of a future amount obtained by discounting at a given rate.

Question 6

What is effective annual rate (EAR)?

Accepted Answer

EAR is the actual annual rate after considering compounding within the year.

Question 7

Calculate simple interest and amount on ₹12,000 at 8% p.a. for 3 years.

Accepted Answer

Given P = 12,000, R = 8% p.a., T = 3 years.

SI, I = (P×R×T)/100 = (12,000×8×3)/100 = 2,880.
Amount, A = P + I = 12,000 + 2,880 = 14,880.

So, SI = ₹2,880 and Amount = ₹14,880.

Question 8

Find compound interest on ₹10,000 at 10% p.a. for 2 years (annual compounding).

Accepted Answer

P = 10,000, R = 10%, T = 2.

Amount A = P(1+R/100)^T = 10,000 × (1.10)^2 = 10,000 × 1.21 = 12,100.
CI = A − P = 12,100 − 10,000 = 2,100.

So, CI = ₹2,100 (Amount = ₹12,100).

Question 9

A sum becomes ₹15,000 in 2 years at 10% p.a. compounded annually. Find the principal.

Accepted Answer

A = 15,000, R = 10%, T = 2.

A = P(1.10)^2 = 1.21P
So P = 15,000/1.21 ≈ 12,396.69.

Principal ≈ ₹12,397.

Question 10

Compute present value of ₹20,000 due after 2 years at 10% p.a. (annual compounding).

Accepted Answer

PV = FV/(1+R/100)^T = 20,000/(1.10)^2 = 20,000/1.21 ≈ 16,528.93.

So PV ≈ ₹16,529.

Question 11

Differentiate between simple interest and compound interest (any three points).

Accepted Answer

Base: SI is calculated on principal only; CI is calculated on principal + accumulated interest.
Growth: SI increases linearly; CI increases faster due to compounding.
Use: SI is used for short-term trade; CI is used in banking/finance for loans and deposits.

Question 12

If nominal rate is 12% compounded monthly, write how EAR is computed and state whether it is > 12% or not.

Accepted Answer

For nominal R = 12% with monthly compounding, n = 12.
EAR = [(1 + (R/100)/n)^n − 1] × 100
= [(1 + 0.12/12)^12 − 1] × 100.
Because compounding is more than once a year, EAR is slightly greater than 12%.

Question 13

Explain present value and future value. Show their relationship with formulas and one numerical example.

Accepted Answer

Present value (PV) is today’s value of a future amount found by discounting. For annual compounding: PV = FV / (1 + R/100)^T.

Future value (FV) is the value of a present sum after earning interest: FV = P (1 + R/100)^T.

Relationship: FV = PV × (1 + R/100)^T and PV = FV / (1 + R/100)^T.

Example: PV of ₹20,000 due after 2 years at 10% is PV = 20,000/(1.10)^2 = 20,000/1.21 ≈ ₹16,529. So ₹16,529 today becomes ₹20,000 after 2 years at 10%.

Question 14

Derive and explain the formula of compound amount when compounding is done n times per year. Give an example.

Accepted Answer

If annual nominal rate is R% compounded n times/year, rate per period = (R/100)/n and number of periods in T years = nT.
Therefore, A = P [1 + (R/100)/n]^(nT).

Example: P=₹10,000, R=12% p.a., T=2 years, compounded half-yearly (n=2):
A = 10,000 [1 + 0.12/2]^(4) = 10,000 (1.06)^4 ≈ 10,000×1.2625 ≈ ₹12,625 (approx).

Question 15

A person invests ₹25,000 at 8% p.a. Calculate (i) amount under SI for 3 years, (ii) amount under CI for 3 years (annual). Compare results.

Accepted Answer

Given P = 25,000, R = 8% p.a., T = 3 years.

(i) SI: I = (25,000×8×3)/100 = 6,000. Amount (SI) = 25,000 + 6,000 = ₹31,000.

(ii) CI (annual): Amount (CI) = 25,000 (1.08)^3. (1.08)^3 = 1.259712. Amount (CI) = 25,000×1.259712 = ₹31,492.80 (approx).

Comparison: CI amount is higher than SI amount by about ₹492.80 because CI includes interest on accumulated interest.

Simple and Compound Interest; Present Value and Future Value

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