Question

Following the birth of a child, a parent wants to make an initial investment P₀ that will grow to $70,000 for the child's education at age 19. Interest is compounded continuously at 6%. What should the initial investment be? Such an amount is called the present value of $70,000 due 19 years from now.

Answer 1

To find the initial investment to reach $70,000 in 19 years at a 6% continuous interest rate, one must calculate the present value using the continuous compounding formula, resulting in an expression that will give the amount needed to be invested today.

Step-by-step explanation:

A parent wants to determine the initial investment (P0) required to grow to $70,000 in 19 years with continuous compounding at a 6% interest rate. To find the present value of the future sum, we use the formula for continuous compounding: P0 = Pe-rt, where P is the future value, r is the interest rate, t is the time in years, and e is the base of the natural logarithm.

The calculation would be: P0 = $70,000 e-0.06×19.

After solving this expression, the parent will know the exact amount to invest today to ensure that there are $70,000 available for their child's education in 19 years.