find the compound interest on Rs15000 at 8% for 9 months, the interest payable quartely

in what time will Rs 64000 amount to Rs 68921 at 5% per annum , interest being compounded half yearly

1. Investment: $15,000 @ 8% for 9mo,compounded quarterly.


Pt = Po(1+r)^n.

r = (8%/4) / 100% = 0.02 = Quarterly
percentage rate expressed as a decimal.

n = 4 comp./yr * 0.75yr = 3 comp. periods.

Pt = 15,000(1.02)^3 = 15,918.12.

Int. = 15918.12 - 15000 = $918.12.

2. Investment: $64000 @ 5%,compounded
semi-annually.

Pt = Po(r+1)^n.

r = (5%/2) / 100% = 0.025 = Semi-annual
% rate expressed as a decimal.

$68,921 = 64,000(1.025)^n,
Divide both sides by 64,000:
(1.025)^n = 68921 / 64000 = 1.0769,
Take log of both sides:
n*log(1.025) = log(1.0769),
0.0107n = 0.03217,
n = 3 comp. periods.

t = 6mo/comp period * 3comp periods =
18 months.

To find the compound interest on Rs 15000 at 8% for 9 months, with interest payable quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt) - P

Where:
A = the final amount including interest
P = the principal amount (initial investment or loan amount)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = time in years

In this case, the principal amount (P) is Rs 15000, the annual interest rate (r) is 8% or 0.08 (in decimal form), and the interest is payable quarterly, which means it's compounded four times a year (n = 4).

First, we need to find the time in years. Since the interest rate is given for 9 months, we convert it to years by dividing it by 12:
t = 9 months / 12 months/year = 0.75 years

Next, we can plug the values into the formula:
A = 15000(1 + 0.08/4)^(4*0.75) - 15000

Simplifying the formula:
A = 15000(1 + 0.02)^3 - 15000
A = 15000(1.02)^3 - 15000
A = 15000(1.0612) - 15000
A = 15918 - 15000
A = 918

Therefore, the compound interest on Rs 15000 at 8% for 9 months, with interest payable quarterly, is Rs 918.