Question

In January, Dana Blakely decided to donate $2,500 to the Riverfront Humane Society. For income tax purposes, she will

not make the donation until next December. If Dana can earn 12% compounded monthly, how much must she invest in
January to have $2,500 in 11 months? (Use Tables 16-1A&B or 16-2A&B or a calculator.)
$2,218.63 invest in January
$2,232.15 invest in January
$2,240.80 invest in January
$2,280.40 invest in January

Answer 1

Dana must invest $2,218.63 in January to have $2,500 in 11 months, using a 12% annual interest rate compounded monthly.

Step-by-step explanation:

To find out how much Dana must invest in January to have $2,500 in 11 months, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the future value
• P is the principal amount
• r is the annual interest rate (as a decimal)
• n is the number of times that interest is compounded per year
• t is the time in years

In this case, we have:

• A = $2,500 (the future value)
• P is the amount Dana wants to invest
• r = 12% or 0.12 (the annual interest rate)
• n = 12 (monthly compounding)
• t = 11/12 (11 months out of a year)

Using the provided information, we can solve for P:

P = A / ((1 + r/n)^(nt))

By substituting the values, we get:

P = $2,500 / ((1 + 0.12/12)^(12*(11/12)))

This simplifies to:

P = $2,218.63

Therefore, Dana must invest $2,218.63 in January to have $2,500 in 11 months.