Theo decides to take a loan and wants to invest the money in either of the following options:
Option 1: The R9000 invested at 8% per month simple interest of 3 years.
Option 2: The R9000 invested at 7% per month compound interest for 3years.
Which of the options will be better , show all calculations.
Option 1
amount after 3 years = 9000 + 9000(3)(.08) = 11,160
Option 2
amount after 3 years = 9000(1.07)^3 = 11,025.39
better question:
after how many years would the two investments yield the same amount ?
(hint: tough question)
To determine which option is better, we need to calculate the final amount in each option at the end of the 3-year period.
Option 1: Simple Interest
The formula for simple interest is: A = P(1 + rt)
Where:
A = final amount
P = principal amount (R9000 in this case)
r = interest rate per period (8% per month)
t = number of time periods (3 years or 36 months)
Using the formula, we can calculate the final amount for Option 1 as follows:
A1 = 9000(1 + 0.08*36)
Option 2: Compound Interest
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (R9000 in this case)
r = interest rate per period (7% per month)
n = number of times interest is compounded per year (monthly compounding, so n = 12)
t = number of time periods (3 years or 36 months)
Using the formula, we can calculate the final amount for Option 2 as follows:
A2 = 9000(1 + 0.07/12)^(12*3)
Now, let's calculate the final amounts for both options:
A1 = 9000(1 + 0.08*36)
= 9000(1 + 2.88)
= 9000(3.88)
= R34,920
A2 = 9000(1 + 0.07/12)^(12*3)
= 9000(1 + 0.00583)^(36)
= 9000(1.00583)^(36)
= R35,685.78
Comparing the final amounts, we can see that Option 2, with compound interest, will result in a higher final amount of approximately R35,685.78. Therefore, Option 2 is the better investment choice.
To determine which option would be better, we need to compare the total amount of money obtained at the end of 3 years for each option.
Option 1: Simple Interest
The formula to calculate simple interest is:
Interest = Principal * Rate * Time
In this case:
Principal = R9000
Rate = 8% per month = 0.08
Time = 3 years = 36 months
Interest = 9000 * 0.08 * 36
Interest = 25920
Total Amount = Principal + Interest
Total Amount = 9000 + 25920
Total Amount = 34920
Option 2: Compound Interest
The formula to calculate compound interest is:
Total Amount = Principal * (1 + Rate)^(Time)
In this case:
Principal = R9000
Rate = 7% per month = 0.07
Time = 3 years = 36 months
Total Amount = 9000 * (1 + 0.07)^36
Total Amount = 9000 * (1.07)^36
Total Amount = 9000 * 2.70336493601
Total Amount = 24330.284424
Comparing the two options:
Option 1: Total Amount = R34920
Option 2: Total Amount = R24330.28
Therefore, option 1 (Simple Interest) would be better as it gives a higher total amount at the end of 3 years.