Question

A bank account has a balance today is $38,000. How much must be deposited at the end of each year to have a balance of $2,000,000 in 29 years if the interest rate is 11%?

Enter your answer as a number rounded to 2 decimal places. An answer of 23.456 would be entered as 23.46.

Answer 1

To have a balance of $2,000,000 in 29 years with an 11% interest rate, you would need to deposit approximately $4,706.46 at the end of each year.

Step-by-step explanation:

To calculate the amount that needs to be deposited at the end of each year to have a balance of $2,000,000 in 29 years with an 11% interest rate, we can use the formula for the future value of an ordinary annuity:

FV = P[(1+r)^n-1]/r

Where FV is the future value, P is the deposit amount, r is the interest rate per period, and n is the number of periods.

Plugging in the given values:

FV = $2,000,000, r = 11%, and n = 29, we can solve for P.

2,000,000 = P[(1+0.11)^29-1]/0.11

Simplifying the equation:

2,000,000 * 0.11 = P[(1+0.11)^29-1]

220,000 = P[(1.11)^29-1]

To find the deposit amount P, we can rearrange the equation:

P = 220,000 / [(1.11)^29-1]

Calculating P, the deposit amount:

P ≈ $4,706.46