If a community clinic invested $3,000 in excess cash today, what would be the value of its investment at the end of three years:
a. at a 12 percent rate compounded semiannually?
B. at a 12 percent rate compounded quarterly?
a) amount = 3000( 1.06)^6 = ...
can you see what I did with the rate and with the time ?
b) let me know what you think about this one
still lose or 30,000(( 1.06)^12=
no,
12% compounded quarterly
means --- the rate is 3% per quarter
and in 3 years there would be 12 quarters,
amount = 3000(1 + .03)^12
= 3000(1.03)^12 = 4277.28
so how am i suppose to find the semiannually at 12
To calculate the future value of the investment, we can use the compound interest formula:
Future Value = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Let's calculate the future value for both scenarios:
a. Compounded Semiannually:
Rate = 12% = 0.12
Number of Compounding Periods = 2 (semiannual compounding)
Time = 3 years
Substituting the values into the formula:
Future Value = $3,000 * (1 + 0.12/2)^(2 * 3)
Future Value = $3,000 * (1 + 0.06)^6
Future Value = $3,000 * (1.06)^6
Future Value ≈ $4,110.14
Therefore, the value of the investment at the end of three years at a 12 percent rate compounded semiannually would be approximately $4,110.14.
b. Compounded Quarterly:
Rate = 12% = 0.12
Number of Compounding Periods = 4 (quarterly compounding)
Time = 3 years
Substituting the values into the formula:
Future Value = $3,000 * (1 + 0.12/4)^(4 * 3)
Future Value = $3,000 * (1 + 0.03)^12
Future Value = $3,000 * (1.03)^12
Future Value ≈ $4,120.21
Therefore, the value of the investment at the end of three years at a 12 percent rate compounded quarterly would be approximately $4,120.21.