Question

For each scenario below, identify the equation that should be used to calculate the requested value. Write the letter corresponding to the formula in the blank provided. DO NOT SET UP OR SOLVE ANY EQUATIONS.

A. Simple interest, I = Prt B. Simple interest, A = P(1 + rt) C. Compound interest D. Annuity E. Payout annuity F. Loan
_____ Ella’s grandparents deposit $50 each month for 15 years into an account earning 5.6% interest. How much money will be in the account after 15 years?
_____ Dante took out a simple interest loan to pay for a new 70-inch television. The interest rate was 4%. If Dante makes 6 payments of $101.66, how much did the television cost?
_____ Jude deposits $1,000 into a 3-year certificate of deposit (CD) that earns 2.1% interest compounded quarterly. How much money will be in the CD at the end of three years?
_____ The Short family is purchasing a home costing $150,000. They make a 20% down payment and finance the rest. They can get a 20-year mortgage at 6.45% interest. What is their monthly payment?
_____ A payday loan company charges $75 interest for a 1-month loan of $125. What interest rate are they charging?

Answer 1

The correct equations to use for the given financial scenarios are Annuity (D) for monthly deposits into an account, Simple Interest (A) for calculating cost of a television with loan payments, Compound Interest (C) for a CD account with quarterly compounding, and Loan (F) for a mortgage. The payday loan scenario is not specified in the options but involves simple interest calculation.

Step-by-step explanation:

The correct equations that should be used to calculate the requested values for the given scenarios are:

• Annuity: Ella’s grandparents deposit $50 each month for 15 years into an account earning 5.6% interest. The calculation for how much money will be in the account after 15 years is an example of an annuity. Therefore, the correct formula is "D".
• Simple interest, I = Prt: Dante took out a simple interest loan to pay for a new 70-inch television. To find out how much the television cost using the monthly payments and interest rate information, a simple interest calculation is needed. The correct formula is "A".
• Compound interest: Jude deposits $1,000 into a 3-year certificate of deposit (CD) that earns 2.1% interest compounded quarterly. To calculate the amount in the CD at the end of the period, the compound interest formula is required, denoted as "C".
• Loan: The Short family’s home purchase involves a mortgage calculation, which is a specialized type of loan calculation. Thus, the correct formula to find the monthly payment is "F".
• To find the annual interest rate charged by the payday loan company for a loan of $125 with a $75 interest charge after one month, we would need to relate the dollar amounts to the simple interest formula and extrapolate the annual rate. However, since the equation is not directly provided in the options, it is not clear which letter to assign. It is likely tied to the kinds of equations involved in "Simple interest", but without the specific formula or letter, it cannot be definitively stated.

For practice on using the simple interest formula, consider the following example:

Example: A $100 deposit at a simple interest rate of 5% held for three years would yield:

$100 × 0.05 × 3 = $15

This calculation shows the total interest, which in this case is $15.