Given:
Final Balance = $160,000
rate = 8% or 0.08
Compounding period = daily = 365 days
time in years = 10
Find: Principal or Initial Amount
Solution:
To determine the principal or the initial amount to be invested in order to have $160,000 at the end of 10 years with the given compounding rate, we have the formula below:
[tex]P=\frac{F}{(1+\frac{r}{m})^{mt}}[/tex]
where:
P = Principal
F = Final Value = $160,000
r = annual rate = 0.08
m = compounding period = 365 days
t = time in years = 10
Let's plug into the formula above the given information.
[tex]P=\frac{160,000}{(1+\frac{0.08}{365})^{365\times10}}[/tex]
Then, solve for P.
a. Add the terms inside the parenthesis and multiply its exponent.
[tex]P=\frac{160,000}{(1.000219178)^{3,650}}[/tex]
b. Apply the exponent to the term in the denominator.
[tex]P=\frac{160,000}{2.22534585}[/tex]
c. Divide the numerator by the denominator.
[tex]P\approx71,898.94[/tex]
Answer:
Therefore, one must invest $71,898.94 in order to produce a final balance of $160,000 at the end of 10 years given that the rate is 8% compounded daily.
