Question

To achieve a future value of $34,250 in 9 years with varying interest rates, how much should be deposited today, considering an annual interest rate of 4 percent for the first 5 years and 4.6 percent for the next 4 years?

Answer 1

To achieve a future value of $34,250 in 9 years with varying interest rates, we can use the formula for compound interest. By substituting the given values into the formula, we can calculate the principal amount that needs to be deposited today.

Step-by-step explanation:

To find the amount that needs to be deposited today, we can use the formula for compound interest:

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

where:

• A is the future value we want to achieve ($34,250)
• P is the principal amount we need to deposit
• r is the interest rate for each period (4% for the first 5 years and 4.6% for the next 4 years)
• n is the number of times the interest is compounded per year (assuming it is compounded annually)
• t is the number of years (9 years)

Substituting these values into the formula, we have:

$34,250 = P(1 + 0.04/1)^(1 * 5) (1 + 0.046/1)^(1 * 4)

Simplifying this equation will give us the principal amount that needs to be deposited today.