🟦 Financial Mathematics

Question 1

What is simple interest and how is it calculated?

Answer 1

Simple interest is interest earned only on the original amount (principal).

Formula: I = P × R × T, where I = interest, P = principal, R = rate, T = time in years.

Question 2

What is compound interest?

Answer 2

Compound interest is interest calculated on the principal and previously earned interest.

Formula: A = P(1 + r)^n, where A = total amount, P = principal, r = rate per period, n = number of periods.

Question 3

What is depreciation and how is it calculated?

Answer 3

Depreciation is the reduction in value of an asset over time.

Formula: Value = Initial × (1 - rate)^time.

Question 4

What is the formula for calculating compound interest with regular deposits?

Answer 4

The formula for compound interest with regular deposits is:

A = P x ( 1 + r/n ) ^ nt + ( d x (( 1 + r/n ) ^nt - 1)) / ( r/n )

Where A = final amount, P = principal, r = interest rate, n = number of compounding periods per year, t = time in years, and d = regular deposit.

Question 5

How do you calculate the amount of money after depreciation over time?

Answer 5

Use the formula for depreciation:

Value = P x ( 1 - r ) ^ t

Where P = initial value, r = depreciation rate, t = time in years.

Question 6

A principal amount of $500 is invested at an annual interest rate of 4% for 3 years. Calculate the simple interest.

Answer 6

To calculate simple interest, use the formula:

I = P × r × t

Where:
I is the interest
P is the principal amount ($500)
r is the annual interest rate (4% or 0.04)
t is the time in years (3 years)

I = 500 × 0.04 × 3 = 60

The simple interest is $60.

Question 7

If $1,000 is invested at 5% annual compound interest, how much will the investment be worth after 4 years if the interest is compounded annually?

Answer 7

To calculate compound interest, use the formula:

A = P × ( 1 + r ) ^ t

Where:
A is the amount (final value)
P is the principal amount ($1,000)
r is the annual interest rate (5% or 0.05)
t is the time in years (4 years)

A = 1000×(1+0.05) = 1000×(1.21550625) = 1215.51

The investment will be worth $1,215.51 after 4 years.

Question 8

A car depreciates in value by 10% per year. If the car is worth $20,000 initially, what will it be worth after 5 years?

Answer 8

For depreciation, use the formula:

V=P×(1−r) ^ t

Where:
V is the value after depreciation
P is the initial value ($20,000)
r is the rate of depreciation (10% or 0.10)
t is the time in years (5 years)

V = 20000×(1−0.10) ^ 5 = 20000×(0.59049) = 11,809.80

The car will be worth $11,809.80 after 5 years.