SOLUTION: Kindly help again 1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520. 2.Calculate compound interest earned of R15000 deposited into bank for 2

Question 1172633: Kindly help again
1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520.
2.Calculate compound interest earned of R15000 deposited into bank for 2 years at 12%p.a
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520.

simple interest formula is:
f = p + p * r * t
f is the future value
p is the present value
r is the interest rate per time period
t is the number of time periods.

in your problem, this becomes:
f = 6000 + 6000 * .06 * t
since f = 8520, this becomes:
8520 = 6000 + 6000 * .06 * t
subtract 6000 from both sides of the equation to get:
2520 = 6000 * .06 * t
simplify to get:
2520 = 360 * t
solve for t to get:
t = 2520 / 360 = 7

it will take 7 years for 6000 to grow to 8520 at 6% per year.
confirm by going back to the formula to get:
f = p + p * r * t becomes:
8520 = 6000 + 6000 * .06 * 7 which becomes:
8520 = 6000 + 360 * 7 which becomes:
8520 = 8520
this confirms the solution is correct.

2. Calculate compound interest earned of R15000 deposited into bank for 2 years at 12%p.a

the compound interest formula is:
f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods

in your problem, the formula becomes:
f = 15000 * (1 + .12) ^ 2
solve for f to get:
f = 18816

.12 was the interest rate per year.
2 was the number of years.
annual compounding was assumed.

since this was only 2 years, it is easy to show the details.

in time period 0, you have 15000
in time period 1, you multiply 15000 * 1.12 to get 16800
in time period 2, you multiply 16800 * 1.12 to get 18816.

the difference between simple interest and compound interest is that, ...
in simple interest, the interest is calculated off the original principle.
in compound interest, the interest is calculate off the principal plus interest from the preceding time period.

to show you the difference, in your second principle, if it was simple interest, the calculations would have been:

f = 15000 + 15000 * .12 * 2 = 18600

the details for that would be:

in time period, you have 15000.
in time period 1, you have 15000 + .12 * 15000 = 16800
in time period 3, you have 16800 + .12 * 15000 = 18600

with compound interest, you earned interest on interest.
with simple interest, you earned interest on the original amount only.

let me know if you have any questions concerning this.
theo

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Kindly help again
1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520.
2.Calculate compound interest earned of R15000 deposited into bank for 2 years at 12%p.a

1.
Calculate the above for T (time)!!
That's it!!
2. Can't be answered without the number of ANNUAL compounding periods!
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