Financial mathematics

• Jun 29th 2007, 01:13 AM
Sane
Financial mathematics
Firstly I would thank Soroban by helping me last time.Thanks again

Guyz please any one help me with the following questions :-

If you took R50 000.00 and invested it in an investment where you were receiving 7% compound interest per annum,

A) What amount of money would you have after 3 years?
B) How would this figure differ if it were not compound.

Remember compound interest is calculated each period on their original principal and all interest accumulated during past period and the compound period can be yearly, semi annually, quarterly or even continuously.

The compound interest formula is fv=pv(1+r / 100)^n.
• Jun 29th 2007, 03:55 PM
Soroban
Hello, Sane!

Quote:

If you took R50 000.00 and invested it at 7% compound interest per annum,

A) What amount of money would you have after 3 years?
B) How would this figure differ if it were not compound?

A) Compound interest formula: . $F \;=\;P(1 + i)^n$

. . where: . $\begin{array}{ccc}P & = & \text{principal invested} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \\ F & = & \text{future value}\end{array}$

We have: . $P = \50,000,\;i = 7\% = 0.07,\;n = 3$

Therefore: . $F \;=\;50,000(1.07)^3 \;=\; \61,752.15$

B) Simple interest formula: . $I \:=\:P \times R \times T$

. . where: . $\begin{array}{ccc} P & = & \text{principal invested} \\ R & = & \text{annual interest rate} \\ T & = & \text{number of years} \\ I & = & \text{interest earned}\end{array}$

We have: . $P = \50,000,\;R = 0.07,\;T = 3$

Hence: . $I \;=\;50,000 \times 0.07 \times 3 \;=\;10,500$ (interest)

Therefore, the future value is: . $\50,000 + 10,500 \;=\;\60,500$

Simple interest always generates less interest than compounding.