Use​ x=1 + r

Question

​, where r is the interest rate paid each year. Write an equation to represent the final amount of each of the following​ 7-year term investments.
Investment​ 1: Deposit​ $3,000 at the beginning of the first year.
Investment​ 2: Deposit​ $2,000 at the beginning of the first​ year, $1,200 at the beginning of the third​ year, and​ $500 at the beginning of the fifth year.
Using the models that you just​ created, which investment option will result in more interest earned at the end of the​ 7-year term if the annual interest rate is 3.7​ percent?
Based on the answer you got for this​ problem, when having the same interest rate and investment​ term, do you think it will be better to invest more at one time or divide the investment into smaller deposits each​ year? Explain your reasoning.

Answer 1

For Investment 1, the equation to represent the final amount after 7 years can be written as:

A1 = 3000 * (1 + r)^7

For Investment 2, the equation to represent the final amount after 7 years can be written as:

A2 = 2000 * (1 + r)^7 + 1200 * (1 + r)^5 + 500 * (1 + r)^3

To determine which investment option will result in more interest earned at the end of the 7-year term if the annual interest rate is 3.7​ percent, we can calculate the final amount for both investments using the given interest rate:

r = 0.037

A1 = 3000 * (1 + 0.037)^7

A2 = 2000 * (1 + 0.037)^7 + 1200 * (1 + 0.037)^5 + 500 * (1 + 0.037)^3

By evaluating these equations, we can determine which investment option results in a higher final amount.

Regarding whether it's better to invest more at one time or divide the investment into smaller deposits each​ year, it depends on the interest rate and the investment term. In some cases, investing a larger amount at one time may result in more interest earned, as in Investment 1. However, in other cases, dividing the investment into smaller deposits each year may yield a higher final amount, as in Investment 2. It's important to consider the specific details of the investment, such as interest rate, investment term, and the timing and amounts of the deposits, to determine the most advantageous strategy.