Final answer:
Using algebra, one can determine the amount invested in two funds based on their interest rates and total interest received. Simple interest can be calculated using the principal, rate, and time. Over time, even small differences in investment returns can result in significant differences in final values due to the power of compounding interest.
Step-by-step explanation:
Calculating Investments and Interest Rates
When Fran invested $700 in two funds at different interest rates, we aim to find out how much was invested in each fund. Here, we are being asked to find the amount invested in each fund, which translates to one thing.
We'll denote the amount invested in the 6% fund as x and the amount invested in the 5.5% fund as y. The sum of these investments is the total amount invested, so we write the equation x + y = 700. The total interest from both investments equals $40.50. Interest from each investment can be represented as 0.06x and 0.055y respectively. So, our second equation based on the total interest is 0.06x + 0.055y = 40.50.
To solve for x and y, we use substitution or elimination to find the values of these variables. In the context of financial terms such as loans or savings, using the formula Interest = Principal × rate × time, we can calculate the interest on different monetary amounts with given rates and time spans.
For example, for a $5,000 loan over three years at a rate of 6%, we'd calculate the total interest as 5000 × 0.06 × 3 = $900. If you receive $500 simple interest from a $10,000 loan for five years, the rate charged is found by dividing the interest by the product of the principal and time: 500 / (10000 × 5) = 0.01, which corresponds to a rate of 1%.
Considering investments and compounding, if Alexx and Spenser both invest $5,000, with one person earning 5% and the other earning 4.75% due to an administrative fee, the difference after 30 years can be obtained by comparing the compounded values of each investment using the formula Principal(1 + interest rate)time.