if you want to save $60000 in 7 years with APR 4% daily compounding and no additional deposits, how much would your initial deposit be
P = Po(1+r)^n = $60,000.
P = $60,000 = Amount after 7 years.
Po = Initial deposit.
r = (4%/360) / 100% = 0.000111111 = Daily % rate expressed as a decimal.
n = 360Comp./yr * 7yrs.=2520 Compounding
periods.
Po(1.000111111)^2520 = 60,000
Po=60000 / (1.000111111)^2520=%45347.74
To calculate the initial deposit required to save $60,000 in 7 years with a daily compounding APR (Annual Percentage Rate) of 4%, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value (the amount you want to save) = $60,000
P is the principal amount (initial deposit)
r is the annual interest rate expressed as a decimal = 4% = 0.04
n is the number of times interest is compounded per year (daily = 365)
t is the number of years = 7
Substituting the given values into the formula, we get:
$60,000 = P(1 + 0.04/365)^(365*7)
Now, we can solve this equation to find the value of P (the initial deposit).
$60,000 = P(1 + 0.000109589)^(2555)
To isolate P, we divide both sides by (1 + 0.000109589)^(2555):
P = $60,000 / (1 + 0.000109589)^(2555)
Using a calculator, we can evaluate the right-hand side of the equation:
P ≈ $50,027.06
Therefore, the initial deposit required to save $60,000 in 7 years with a 4% daily compounding APR would be approximately $50,027.06.