Answer: To calculate the compound interest and amount for a given principal, interest rate, and time period, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount (principal + interest)
P = the principal (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the investment is held
a. Principal = $5,900; Time = 2 years; Rate = 14%
n = 2 (since the interest is compounded half-yearly)
t = 2
r = 0.14
A = 5900(1+0.14/2)^(22)
A = 5900(1+0.07)^4
A = 59001.07^4
A = 5900*1.298844
A = 7,638.21
So the final amount, including interest, would be $7,638.21
b. Principal = $7,800; Time = 6 years; Rate = 18%
n = 2 (since the interest is compounded half-yearly)
t = 6
r = 0.18
A = 7800(1+0.18/2)^(26)
A = 7800(1+0.09)^12
A = 78001.09^12
A = 7800*2.05832
A = 16,093.32
So the final amount, including interest, would be $16,093.32
Please note that the above calculations are based on the compound interest formula and the assumption that the interest is compounded half-yearly, without taking into account any fees, taxes or any other associated cost.
Explanation: