Final answer:
To find the nominal interest rate, calculate the total interest earned over the period and solve the simple interest formula. With a quarterly payment of $10 for 5 years on a $1,000 principal, the nominal annual interest rate is 4%.
Step-by-step explanation:
To calculate the nominal interest rate for a savings account where $1,000 is deposited and $10 is paid every quarter, we can use the formula for simple interest:
Interest = Principal × rate × time
In this scenario, the interest earned each quarter is $10. Since there are four quarters in a year, the total annual interest will be $10 × 4 = $40. The total time the money is deposited is 5 years. Therefore, the total interest earned over the 5 years is $40 × 5 = $200.
Now, we can plug in the values to the simple interest formula to solve for the rate:
Total Interest = Principal × rate × time
$200 = $1,000 × rate × 5
Divide both sides by the principal ($1,000) and the time (5 years) to solve for the nominal annual interest rate:
$200 / ($1,000 × 5) = rate
$200 / $5,000 = rate
0.04 = rate
Thus, the nominal interest rate is 4% per annum.