Question

Compound Interest Project Goal:

The goal is to use compound interest formulas to investigate and compare savings situations while using your writing skills to clearly communicate the solution. Role: You are the financial consultant for a young couple who are in need of financial advice. Situation: In this recession, everyone is looking to earn the most they can on their savings. You have been hired as a financial consultant to help people determine the best options for their savings plans. Utilizing your compound interest skills, you need to convince the young couple of the best option for their savings. Scenario: Joe and Josephina Nestegg wish to invest in a no-risk savings account. They currently have $25,000 in an account bearing 5 1/4 % annual interest, compounded continuously. The following options are available to them:
i. keep the money in the account they currently have
ii. invest the money in an account bearing 5 7/8 % annual interest, compounded annually
iii. invest the money in an account bearing 5 1/2 % annual interest, compounded quarterly
Determine the equation for the value for the investment as a function of time for each of the three options. (Calculations)

Answer 1

The equation for the value of the investment as a function of time for each option is determined using the compound interest formula .Applying the formula we get equations Ai = $25,000(1 + 5.25/100)^(1t),Aii = $25,000(1 + 5.875/100)^(1t),Aiii = $25,000(1 + 5.5/100)^(4t) .

Step-by-step explanation:

To determine the equation for the value of the investment as a function of time for each of the three options, we can use the compound interest formula:

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

Where:

• A is the future value of the investment
• P is the principal amount
• r is the annual interest rate
• n is the number of times the interest is compounded per year
• t is the number of years

Applying the formula to each option:

1. For option i, the equation is:
2. Ai = $25,000(1 + 5.25/100)^(1t)
3. For option ii, the equation is:
4. Aii = $25,000(1 + 5.875/100)^(1t)
5. For option iii, the equation is:
6. Aiii = $25,000(1 + 5.5/100)^(4t)