Bongiwe invested a certain amount into a savings account at 6,5% compound
interest per annum. If the final amount is R15 300 after 5 years, how much did
she originally inves
To calculate the original investment amount, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal amount (original investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case:
A = R15,300
r = 6.5% = 0.065 (as a decimal)
n = 1 (compounded annually)
t = 5 years
Using the formula, we can rearrange it to solve for P:
P = A / (1 + r/n)^(n*t)
P = R15,300 / (1 + 0.065/1)^(1*5)
P = R15,300 / (1 + 0.065)^(5)
P = R15,300 / (1.065)^5
P ≈ R11,582.03
Therefore, Bongiwe originally invested approximately R11,582.03.
To find out how much Bongiwe originally invested, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (R15,300)
P = Principal amount (unknown)
r = Interest rate per year (6.5% or 0.065)
n = Number of times interest is compounded per year (1 for annually)
t = Number of years (5)
Let's plug in the given values into the formula and solve for P:
15,300 = P(1 + 0.065/1)^(1 * 5)
15,300 = P(1 + 0.065)^5
15,300 = P(1.065)^5
15,300 = P(1.352)
15,300/1.352 = P
11,309.07 = P
Therefore, Bongiwe originally invested R11,309.07.