Personal Arithmetic

Interest: 

Interest is a payment made for saving or borrowing money. The extra amount is called interest. 

Simple Interest: 

A simple interest is an interest calculated on a fixed yearly rate. 

Example 1.1.1:

Find the simple interest on a loan of ₦40 000 for 1 year at 5% per annum.

Solution 

Yearly interest = \( \scriptsize 5 \% \: of \: N40 000 \\ = \frac{5}{100} \scriptsize \: \times \: N40 000 \\ \scriptsize = N2,000  \)

Simple Interest for 5 years = \( \scriptsize N2,000 \: \times \: 5 \\ =   \scriptsize N10,000\)

Alternatively, you can use the formula for simple interest

Simple Interest = \( \frac{Principal \: \times \: Rate \: \times \: Time}{100} \)

Where;

Principal: Is the original amount invested, saved or borrowed. It is also called capital. 
Rate: Rate is the percentage of the principal charged for saving or borrowing money. 
Time: This is the duration of the investment or saving. 

In the example above,

Principal, P = ₦40,000

Rate, R = 5%

Time, T = 1 year

Substitute these values into the formula;

Simple Interest = \( \frac{Principal \: \times \: Rate \: \times \: Time}{100} \)

Simple Interest = \( \frac{40,000 \: \times \: 5 \: \times \: 1}{100}\\ = \frac{400 \: \times \: 5}{1} \\ = \scriptsize N2,000\)

Simple Interest S.I. = \( \frac{PRT}{100} \)

Amount = Principal + Interest 

The total amount to be paid by the borrower to the lender is called the Amount.

• In example 1 above, the money borrowed from the lender or the principal is N40,000.

• After one year the interest on the money borrowed was N2,000

• So the money to be paid back by the borrower to the lender after a year will be;
  • Amount = Principal + Interest
  • Amount = N40,000 + N2,000
  • Amount = N42,000

Example 1.1.2: 

Find the simple interest and amount on ₦10 000 for 2 years at 4% per annum 

Solution 

Interest for 4% of ₦10 000 

= \( \frac{4}{100} \scriptsize \: \times \: N10,000 \)

= \( \scriptsize N400 \)

Simple Interest = Interest for 2 years 

= \( \scriptsize N400 \: \times \: 2 \)

= \( \scriptsize N800 \)

Or

Simple Interest S.I. =\( \frac{PRT}{100} \)

Simple Interest S.I. = \( \frac{10,000 \: \times \: 4 \: \times \: 2}{100} \)

= \( \scriptsize 100 \: \times \: 4 \: \times \: 2 \)

= N800 

Amount = Principal + Interest 

= N10000 + N800 

Amount = N10,800

Example 1.1.3:

A man borrows N40 000 on a short-term loan and is charged an interest of N1 on each N10 per week. 

How much does he pay back altogether, if he borrows the money; 
(a) For 1 week? 
(b) For 3 weeks?
(c) For 10 weeks?

Solution 

(a) If the man is charged N1 for each N10 per week, then he will be charged  

\( \frac{N40,000}{10} \) for 1 week as interest. 

Interest for 1 week = \( \frac{N40,000}{10} \)

Interest for 1 week = N4,000

This means that there are “4,000” 10′ Nairas in N40,000

If the man is charged N1 for each N4,000 = 1 × 4000 = N4,000
If he was charged 2N it will be 2 × 4000 = N8,000

Amount paid back = N40000 + N4000 = N44000

(b) Interest for 3 weeks = Interest in one week × 3 

N4000 × 3 = N12,000

Amount paid back = N40,000 + N12,000 = N52,000

(c) Interest for 10 weeks = Interest for one week × 10

= N4000 × 10 = N40,000

Amount paid back = N40,000 + N40,000 

= N80,000