How much must be deposited today into the following account in order to have$120000 in 14 years ? No additional deposits are made. An account with quarterly compounding and an APR of 7.4% ?
To calculate the amount that needs to be deposited today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account ($120,000 in this case)
P = the principal amount (the amount to be deposited today)
r = the annual interest rate (7.4% in this case)
n = the number of times interest is compounded per year (quarterly compounding, so n = 4)
t = the number of years (14 years in this case)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Plugging in the values, we have:
P = 120000 / (1 + 0.074/4)^(4*14)
Now we can calculate the result:
P = 120000 / (1 + 0.0185)^(56)
P = 120000 / (1.0185)^56
To solve this equation, you can use a scientific calculator or an online calculator. After the calculation, the result will be the amount that needs to be deposited today in order to have $120,000 in 14 years.
Let X be the money must be deposited today.
120000=X*(1+(7.4%/4))^(4*14)
120000=X*2.791372958...
X=42989.59753
So in order to have $120000 in 14 years, at least deposit $42990 in to bank.