 Mathematics of finance

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Mathematics of finance
Chapter 5 Mathematics of finance

Mathematics of Finance
Simple interest Simple Discount Compound Interest Annuity

5.1 SIMPLE INTEREST

objectives At the end of this topic, students should be able to:
Find the simple interest and amount Find exact and ordinary interest Solve problems involving finding time, simple interest rate and principal

Definition SIMPLE INTEREST COMPOUND INTEREST
Interest (I ) – the fee charged for having the use of money. when you get a loan from a bank, the bank charges you interest for using its money. If you invest your money in a bank, the bank pays you interest for using your money. SIMPLE INTEREST COMPOUND INTEREST

Simple interest (I) Principal (P)
interest that is paid solely on the principal. With simple interest, the interest is not reinvested, so the interest earned each period only on the original principal. Principal (P) the total amount of money borrowed or invested.

Formulae The simple interest, I for a principal, P for t years at an annual rate , r is given by the formula: I = Prt I = simple interest (amount) r = simple interest rate per year t = time or term in years P = principal (present value)

Therefore, the amount, S can be calculated by using the formula
S = P + I (principal + interest) S = P(1 + rt)

Example 1 Ahmad deposited RM1000 in a bank at 8% per annum for three years period. Find the amount of simple interest that will be obtained by Ahmad.

Solution year Principal (P) Interest (I) Future amount S = P + I 1
1000 80 2 1080 3 1160

Solution (by using the formula)

Example 2 Rohana deposits RM 550 at 6% simple interest. How much interest that will Rohana earn after 3 years and 8 months, hence, find the future value.

Solution P = r = t = I = S =

Example 3 How long will it take for a sum of
money to double at a simple interest rate of 5% per year?

Ordinary interest (approximate time)
Exact interest Interest is calculated based on 365 days per year or 366 days for the leap year Ordinary interest (approximate time) Interest is calculated based on 360 days per year. It is considered that there are 30 days for a month.

Example 4 Compute a) exact interest and b) ordinary interest
on RM 2000 at 8% for 175 days

Example 5 On 1st January 2008, Hidayat saved RM1200 in an account that pays 8.6% per annum simple interest. Three years later, he added another RM500 into the account. Find the amount in his account on 1st January 2013.

Example 6 A certain sum of money is invested now. This investment will be worth RM5500 after 15 months and RM5800 after 24 months. Find the original principal and the simple interest rate that was offered.

Example 7 Mariana invested RM in two accounts; some at 12% per annum and the rest at 8% per annum. Her total interest for one years was RM3200. How much was invested at each rate?

Solution S = RM30000 + RM3200 = RM33200 r1 = 12% r2 = 8% t = 1 year
Solve both equations simultaneously, Thus, P1 = RM P2 = RM10000

Example 8 At what rate of simple interest will a sum of money triple itself in six years ?

Example 9 Zamri needs RM6000 in three years time. Now, he saves RM3000 in an account that pays 7% per annum simple interest. Find the amount that he must save two years from now so that he can accumulate the RM6000.