How much down is needed to get to 25000 at 8 percent interest compounded semianually for 3 .5 years
A = p( 1 + r/n)^t*n
t = 3.5*2 = 7
r = 0.08/2 = 0.04
A = 25000( 1+ 0.04)^7
A = 25000( 1.04)^7
A = $32,898.29
P = Po(1+r)^n
P = $25,000
Po = ? = Initial principal.
r = (8%/2)/100% = 0.04 = Semi-annual %
rate expressed as a decimal.
n = 2Comp./yr. * 3.5yrs. = 7 Compounding
periods.
P = Po(1.04)^7 = 25,000
Po = 25,000/1.04^7 = $18,997.95 Down.
To calculate the amount needed to reach $25,000 at 8% interest compounded semiannually over a period of 3.5 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value
P is the principal (initial amount)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, we want to find the amount needed as the future value (A), the principal is what we are trying to determine, the interest rate (r) is 8% or 0.08, interest is compounded semiannually, so n = 2 (twice a year), and t = 3.5 years.
The formula can be rearranged to solve for P:
P = A / (1 + r/n)^(nt)
Plugging in the given values:
P = 25000 / (1 + 0.08/2)^(2 * 3.5)
Now, let's solve this equation:
P = 25000 / (1.04)^(7)
P = 25000 / 1.41493
P ≈ $17,658.41
Therefore, approximately $17,658.41 needs to be deposited to yield $25,000 after 3.5 years at an 8% interest rate compounded semiannually.