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 invest
To find out how much Bongiwe originally invested, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal/initial investment
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Given:
A = R15,300
r = 6.5% = 0.065
t = 5 years
Now we can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
P = 15300 / (1 + 0.065)^5
P ≈ R11,447.09
Bongiwe originally invested approximately R11,447.09.
To calculate the original amount invested by Bongiwe, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (R15,300)
P = Principal amount (original investment)
r = Annual interest rate (6.5% or 0.065)
n = Number of times interest is compounded per year (assuming once per year)
t = Number of years (5)
Plugging in the values we know, the formula becomes:
15,300 = P(1 + 0.065/1)^(1*5)
Simplifying further:
15,300 = P(1.065)^5
To isolate the principal amount (P), divide both sides of the equation by (1.065)^5:
P = 15,300 / (1.065)^5
Calculating this value:
P ≈ 12,500.86
Therefore, Bongiwe originally invested approximately R12,500.86.