The desired future accumulated amount is 120,000 after 7 years invested in an account with 7% interest compound quarterly. How much should you invest presently.
We can use the formula for compound interest to solve for the present value:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the annual interest rate, n is the number of times the interest is compounded during the year, and t is the number of years.
In this case, we have:
A = 120,000
r = 7% = 0.07
n = 4 (quarterly compounding)
t = 7
So we can solve for P:
P = A / (1 + r/n)^(nt)
P = 120,000 / (1 + 0.07/4)^(4*7)
P = 78,313.61
Therefore, you should invest $78,313.61 presently to accumulate $120,000 after 7 years invested in an account with 7% interest compound quarterly.
To calculate the present amount you should invest to reach a desired future accumulated amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Future accumulated amount
P = Present amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, we have:
A = $120,000
r = 7% = 0.07 (as a decimal)
n = 4 (since interest is compounded quarterly)
t = 7 years
We need to solve for P.
120,000 = P(1 + 0.07/4)^(4*7)
Simplifying the right side of the equation:
120,000 = P(1.0175)^(28)
Next, divide both sides by (1.0175)^(28):
P = 120,000 / (1.0175)^(28)
Using a calculator, we find that (1.0175)^(28) is approximately 1.135.
P = 120,000 / 1.135 ≈ $105,538.61
Therefore, you should invest approximately $105,538.61 presently to reach a desired future accumulated amount of $120,000 after 7 years.