SOLUTION: Find the present value and the future value of semi-annual payments of 105,000 pesos with an interest rate of 12% compounded annually for 5 years.
Question 1188769: Find the present value and the future value of semi-annual payments of 105,000 pesos with an interest rate of 12% compounded annually for 5 years. Answer by Theo(13342) (Show Source):
the growth factor per semi-annual period is (1.12) ^ (1/2) = 1.058300524.
the interest rate per semi-annual period is that minus 1 = .0583005244.
multiply that by 100 and the interest rate per semi-annual period is 5.830052443%.
percent divided by 100 = rate.
rate * 100 = percent.
the result of using the arachnoid calculator are shown below:
inputs are everything except pv.
output is pv.
inuts are everything except fv.
output is fv.
number of payments is equal to 5 years * 2 semi-annual periods per year = 10 semi-annual periods.
interest rate per time period is equal to 12% per year compounded annually.
to find the interest rate per semi-annual period, do the following:
12% / 100 = .12 per year.
.12 + 1 = 1.12 growth factor per year
1.12 ^ (1/2) = 1.058300524 growth factor per semi-annual time period.
subtract 1 from that to get interest rate of .058300524 per semi-annual time period.
multiply that by 100 to get 5.830052443% interest rate per semi-annual time period.
percent = rate * 100
rate = percent / 100
the number of time periods and interest rate percent per time period are the same in both the present value and the fuure value analysis.
interest rate per semi-annual time period is not the same when you compound annually than when you compound semi-annually.
when you compound annually, the interest rate per semi-annual time period is ((1.12 ^ .5) - 1) * 100 = 5.830052443%.
when you compound semi-annually (twice a year), the interest rate per semi-annual time period is 12% / 2 = 6%.
