Your brother has offered to give you ​$115​, starting next​ year, and after that growing at 2.5 % per year for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 6.3 % annual interest rate so long as you have money in the account.
a. How much money will you need to deposit into the account​ today

To calculate how much money you would need to deposit in the account today, we need to determine the **present value** (PV) of the cash flows your brother is offering, discounted at the bank's interest rate.

The cash flows are growing at a rate of 2.5% per year, starting from $115. The formula for the present value of growing annuities is:

\[
PV = \frac{C_1}{r - g} \times \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right]
\]

Where:
- $C_1 = 115$ (the first payment next year),
- $r = 6.3\% = 0.063$ (the bank's annual interest rate),
- $g = 2.5\% = 0.025$ (the growth rate of the payments),
- $n = 20$ years (the number of payments).

Now let's calculate the present value.You would need to deposit approximately **$1,565.06** into the account today to generate the same cash flows that your brother is offering over the next 20 years.

Would you like more details or have any questions?

Here are some related questions you might want to explore:
1. How does the present value change if the interest rate increases?
2. What happens if the growth rate of payments is higher than the interest rate?
3. How much will the total payments be after 20 years?
4. What if the payments start immediately instead of next year?
5. How does inflation affect the real value of these future payments?

**Tip:** When comparing offers involving future cash flows, always discount them to present value to understand their true worth today.

Your brother has offered to give you $115, starting next year, and after that growing at 2.5% per year for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 6.3% annual interest rate so long as you have money in the account. How much money will you need to deposit into the account today?

Find out how to calculate the present value of an offer that involves growing annual payments starting from $115 with a 2.5% increase each year over 20 years, discounted at a 6.3% bank interest rate. Learn the key formulas and financial concepts like the time value of money and growing annuities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation