Answer:
First deposit will be $11,213.87
Explanation:
To derive how much the first deposit must be, the deposit can be derived by using payment formula for growing annuity
P = FV x (r - g) / [(1 + r)^n - (1 + g)^n]
When FV = $1,000,000
r = 7%
g = 3%
n = 25
Hence, First payment will be:
P = 1,000,000 * (7% - 3%) / (1.07^25 - 1.03^25)
P = 1,000,000 * 4% / 5.427433 - 2.093778
P = 40,000 / 3.333655
P = 11998.842
P = $11,998.84
However, this formula is applicable when the payments are made at the end of the year. In this case the payments are upfront, occurring today. We need to adjust this first payment to reflect the early payment.
Hence, first payment = $11,998.84 / (1 + 7%)
First payment = $11,998.84 / (1 + 0.07)
First payment = $11,998.84 / 1.07
First payment = 11213.8691588785
First payment = $11,213.87
