Question

Inflation austin is planning his new-born girl's university education. he wants to give his girl $50,000 (in today's dollars) per year for 5 years, from her 19th birthday. austin starts to deposit an equal amount sa every year from her first birthday till her 18th birthday to a savings account. if the expected annual inflation rate is 3% and the interest rate earned on the savings account is 10%, what is the amount of the annual deposit a?

Answer 1

To find the amount of the annual deposit a, we can use the formula for future value of an ordinary annuity: FV = A * [(1 + r)^(n-1)] / r. Solving for A, we find that the annual deposit A is approximately $2,699.96.

Step-by-step explanation:

To find the amount of the annual deposit a, we can use the formula for future value of an ordinary annuity:

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

Where FV is the future value, A is the annual deposit, r is the interest rate earned, and n is the number of years.

In this case, we want to find the deposit amount A. The future value FV is $50,000 (assuming the amount is adjusted for inflation), the interest rate r is 10%, and the number of years n is 18. We can rearrange the formula to solve for A:

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

Plugging in the values, we get:

A = $50,000 * (0.10 / [(1 + 0.10)^(18-1)])

Simplifying the equation, we find that the annual deposit A is approximately $2,699.96.