a couple deposits $4000 in an account that pays 5.9% annual interest compounded quarterly. What will be the value of their investment after 20yrs
20*4 = 80 periods
rate per period = .059/4 = .01475
1.01475^80 = 3.226448959
*4000 = $12,905.80
To calculate the value of the investment after 20 years with compound interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the future value of the investment (the value after 20 years)
P is the initial principal amount ($4000)
r is the annual interest rate (5.9% or 0.059)
n is the number of times interest is compounded per year (quarterly, so 4)
t is the number of years (20)
Let's substitute the given values into the formula and calculate the future value:
A = 4000 * (1 + 0.059/4)^(4*20)
First, calculate the value inside the parentheses: (1 + 0.059/4) = 1.01475
A = 4000 * (1.01475)^(80)
Next, raise that value to the power of the number of compounding periods: (1.01475)^(80) ≈ 1.979311
A = 4000 * 1.979311 ≈ $7,917.24
Therefore, the value of their investment after 20 years will be approximately $7,917.24.