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?
What is 4000(1+.059/4)^80 ?
(that would take them through about 1/4 of the first year of their retirement)
I hope you mean that they deposit $4000 every quarter year for 20 years.
if that is the case they would have
4000 (1 + .059/4)^80 - 1)/(.059/4)
= $603 782.77
(that's more like it)
To calculate the value of the investment after 20 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (or value) of the investment
P = the principal amount (or initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $4000
r = 5.9% = 0.059 (since it's given as a percentage)
n = 4 (compounded quarterly, so 4 times a year)
t = 20 years
Now, let's calculate the value of the investment:
A = $4000 (1 + 0.059/4)^(4*20)
A = $4000 (1 + 0.01475)^(80)
A = $4000 (1.01475)^(80)
A = $4000 (1.868063164)
A ≈ $7,472.25
Therefore, the value of their investment after 20 years will be approximately $7,472.25.