To save for their retirement, a couple deposits $4000 in an account that pays 5.9% annual interest compounded quarterly. What will be the value of their investment after 20 yr?
Pt = Po * (r + 1)^n.
Pt = value after time t(20yrs),
Po = Initial investment,
r = Quarterly percentaqge rate(QPR)
expressed as a decimal,
n = the number of compounding periods.
r = 0.25 * 5.9 = 1.475 % = 0.01475,
n = 20 yrs / 0.25 yr = 80.
Pt = 4000 * (0.01475 + 1)^80 = 12905.80.
To find the value of their investment after 20 years, 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 deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $4000
r = 5.9% = 5.9/100 = 0.059 (as a decimal)
n = 4 (compounded quarterly)
t = 20 years
Substituting the given values into the formula:
A = 4000(1 + 0.059/4)^(4*20)
Next, we need to simplify the equation by performing the calculations inside the parentheses and then raising it to the power:
A = 4000(1 + 0.01475)^80
A = 4000(1.01475)^80
Now, we can use a calculator to evaluate (1.01475)^80 and multiply the result by $4000 to find the future value of the investment.