A term investment of 85000, is madr for 10 years at 4.25% interest. Find the value of the investment at maturity if interest is compoundes quarterly?
To find the value of the investment at maturity with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $85,000, the annual interest rate (r) is 4.25% (0.0425 as a decimal), the number of times the interest is compounded per year (n) is 4 (quarterly compounding), and the number of years (t) is 10.
Let's substitute the values into the formula and calculate the future value (A):
A = 85000(1 + 0.0425/4)^(4*10)
A = 85000(1 + 0.010625)^(40)
A = 85000(1.010625)^(40)
A ≈ 127298.71
Therefore, the value of the investment at maturity, with quarterly compounding, is approximately $127,298.71.