Question
Find the accumulated value of an annuity of K 7 500 invested at the end of each quarter for
five years at an annual rate of 8% compounded quarterly
five years at an annual rate of 8% compounded quarterly
Answers
GPT 3.5
To find the accumulated value of the annuity, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
Where:
FV = Future Value
P = Payment amount per period (in this case, K 7,500)
r = Annual interest rate (8% or 0.08)
n = Number of compounding periods per year (4, since it is compounded quarterly)
t = Number of years (5 years)
Plugging in the values:
FV = 7500 * ((1 + 0.08/4)^(4*5) - 1) / (0.08/4)
FV = 7500 * ((1 + 0.02)^20 - 1) / 0.02
FV = 7500 * (1.05^20 - 1) / 0.02
FV = 7500 * (2.653297705 - 1) / 0.02
FV = 7500 * 1.653297705 / 0.02
FV = 7500 * 82.66488525
FV = K 619,985.14
So, the accumulated value of the annuity after 5 years would be K 619,985.14.
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
Where:
FV = Future Value
P = Payment amount per period (in this case, K 7,500)
r = Annual interest rate (8% or 0.08)
n = Number of compounding periods per year (4, since it is compounded quarterly)
t = Number of years (5 years)
Plugging in the values:
FV = 7500 * ((1 + 0.08/4)^(4*5) - 1) / (0.08/4)
FV = 7500 * ((1 + 0.02)^20 - 1) / 0.02
FV = 7500 * (1.05^20 - 1) / 0.02
FV = 7500 * (2.653297705 - 1) / 0.02
FV = 7500 * 1.653297705 / 0.02
FV = 7500 * 82.66488525
FV = K 619,985.14
So, the accumulated value of the annuity after 5 years would be K 619,985.14.