jeromeborrowed an amount of money on 16th june 1999. he has to pay Ri7500 back on 25th feb 2000. what was the amount borrowed if simple interest of 26% is chargedd?
qn 2. For 20yrs sidney deposited R200 every month into an account. this account earned 15% intrest compounded monthly. After this period of time sidney withdrew his money, paid his tax of 45% on the amount and re-invested the money for 5yrs at an intrest rate of 16% per annum compounded quarterly. the amount that sidney will receive at the end of the five years equals:
What does the Ri (or R) stand for? Chinese Renmibi? British Pounds?
From June 16 to Feb 25 of the next year is 195 days. The interest due will be
195/365 x 0.26 x (Principle)= 7500
If that is an interest-only payment, the loan principle (the original amount borrowed) is 53,994. You decide what the currency units are.
R stands for South African Rands
To find the amount borrowed in the first question, we can use the simple interest formula:
Simple Interest = Principal x Rate x Time
In this case, we are given the interest amount (Ri7500), the rate (26%), and the time in annual terms (19/365 years). We need to find the principal amount.
Let's break down the calculation step by step:
Step 1: Convert the time to years:
19 days / 365 days = 0.0521 years
Step 2: Plug the values into the formula and solve for the principal:
Ri7500 = Principal x 0.26 x 0.0521
Divide both sides of the equation by (0.26 x 0.0521) to isolate the principal:
Principal = Ri7500 / (0.26 x 0.0521)
Calculating this, we find:
Principal = Ri7500 / 0.013546
Principal ≈ R553,357.16
Therefore, if a simple interest rate of 26% is charged, Jerome borrowed approximately R553,357.16.
Now let's move on to the second question:
To calculate the final amount Sidney will receive at the end of the five years, we'll need to use compound interest formulas and make a few calculations. Here's the breakdown:
Step 1: Calculate the future value of the first 20 years of monthly deposits:
We'll use the compound interest formula:
Future Value = P(1 + r/n)^(nt)
Where:
P = monthly deposit amount (R200)
r = annual interest rate (15% or 0.15)
n = number of compounding periods per year (12)
t = number of years (20)
Substituting the values into the formula, we have:
Future Value = R200(1 + 0.15/12)^(12*20)
Calculate this value.
Step 2: Calculate the amount after paying taxes:
After Sidney withdraws the money, they will have to pay taxes of 45% on the amount. Subtract 45% from 100% to get the net percentage: 100% - 45% = 55%
Multiply the future value from step 1 by 55% to calculate the amount after taxes.
Step 3: Calculate the final future value after reinvesting for 5 years:
Using the compound interest formula again:
Future Value = P(1 + r/n)^(nt)
Now, we'll use the following values:
P = amount after taxes from step 2
r = annual interest rate (16% or 0.16)
n = number of compounding periods per year (4, as it is compounded quarterly)
t = number of years (5)
Substituting these values, calculate the future value.
The resulting value will be the amount that Sidney will receive at the end of the five years.