Question

You need to have $30,250 in 17 in years. You can earn an annual interest rate of 4 percent for the first 5 years, 4.6 percent for the next 4 years, and 5.3 percent for the final 8 years. how much do you have to deposit today?

Answer 1

The amount that has to be deposited today is $6205.63

Step-by-step explanation:

The given parameters are;

The annual interest rate for the first 5 years = 4 percent

The annual interest rate for the next 4 years = 4.6 percent

The annual interest rate for the final 8 years = 5.3 percent

Let the amount deposited be X, we have;

X × (1 + 0.04)⁵ + X × (1 + 0.04)⁵×(1.046)⁴ + X × (1 + 0.04)⁵×(1.046)⁴ ×(1.053)⁸ = $30,250

X ((1.04)^5 + (1 + 0.04)^5×(1.046)^4 + (1 + 0.04)^5×(1.046)^4 ×(1.053)^8) = $30,250

X × 4.875 = $30,250

X = $30,250/$4.875 = $6205.63

The amount that has to be deposited today = $6205.63.