Question 1178092: At what rate compounded quarterly will Php 14, 000 become Php 16, 500 for 3 years Found 2 solutions by Theo, mananth:Answer by Theo(13342) (Show Source):
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.
the formula becomes:
16500 = 14000 * (1 + r) ^ 12
r is the interest rate per quarter.
n is the number of quarters = 3 * 4 = 12.
p is equal to 14000.
f is equal to 16500.
divide both sides of the formula by 14000 to get:
16500 / 14000 = (1 + r) ^ 12
take the third root of both sides of the equation to get:
(16500 / 14000) ^ (1/12) = 1 + r
solve for 1 + r to get:
1 + r = (16500 / 14000) ^ (1/12) = 1.013786085.
subtract 1 from that to get:
interest rate of .013786085 per quarter.
multiply that by 4 to get:
nominal interest rate per year = .05514434 per year.
that's the same as 5.514434 per cent nominal interest rate per year.
you could also solve this by calculator as shown below:
inputs are;
output is:
the result from the calculator is the percent interest rate per quarter.
multiply that by 4 to get nominal interest rate percent of 5.514432 per year.
the very slight difference between the manually calculated results and the financial calculator results is due to rounding of the intermediate results in the display of the calculator.
You can put this solution on YOUR website! Solving for rate r as a decimal
r = n[(A/P)^(1/nt) - 1]
r = 4 × [(16,500.00/14,000.00)^(1/(4)(3)) - 1]
r = 0.0551444
Then convert r to R as a percentage
R = r * 100
R = 0.0551444 * 100
R = 5.514%/year
