Show all the formulae and steps of the calculations. If you are using acalculator, show all the calculator inputs. You are required to round offthe final answer only, to two (2) decimal places, e.g., 56.837 = 56.84.• Please do not round off the answers of the calculations before the finalanswer. No marks will be awarded if you round off intermediate workingsbefore the final answer.2.1 You have a lump sum of R500 000 to invest. The bank offers you aninterest rate of 6% per annum.2.1.1 Calculate how much you will receive after five (5) years ifinterest is compounded weekly
Question
Show all the formulae and steps of the calculations. If you are using acalculator, show all the calculator inputs. You are required to round offthe final answer only, to two (2) decimal places, e.g., 56.837 = 56.84.• Please do not round off the answers of the calculations before the finalanswer. No marks will be awarded if you round off intermediate workingsbefore the final answer.2.1 You have a lump sum of R500 000 to invest. The bank offers you aninterest rate of 6% per annum.2.1.1 Calculate how much you will receive after five (5) years ifinterest is compounded weekly
Solution
To calculate the future value of an investment with weekly compounding interest, we can use the formula for compound interest:
FV = P * (1 + r/n)^(nt)
where: FV = future value of the investment P = principal amount (the initial amount of money) r = annual interest rate (in decimal form) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, P = R500 000, r = 6% or 0.06, n = 52 (since interest is compounded weekly), and t = 5 years.
Substituting these values into the formula, we get:
FV = 500000 * (1 + 0.06/52)^(52*5)
Now, calculate the expression inside the parentheses:
1 + 0.06/52 = 1.00115384615
Then, raise this result to the power of 260 (which is 52 weeks/year * 5 years):
(1.00115384615)^260 = 1.348563461
Finally, multiply this result by the initial principal amount:
FV = 500000 * 1.348563461 = R674281.73
So, after 5 years of weekly compounded interest, you will receive approximately R674,281.73.
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