Final answer:
To calculate compounded interest and savings annuities, you can use specific formulas that incorporate the principal, interest rate, time, and the number of compounding periods. Subtracting the initial deposit from the final amount gives you the interest earned. For annuities, determining the period deposit based on desired future value employs a different formula, and the interest earned is the total deposits minus the future value.
Step-by-step explanation:
Calculating Compound Interest and Savings Annuity
To answer question (a), you would use the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is time in years. Plugging in the values, you would have A = 4000(1 + 0.025/1)^(1*20), which gives you the final amount in the account after 20 years.
For question (b), the interest earned is simply the final amount minus the initial deposit, so you would subtract $4000 from the result of question (a) to find the interest earned over 20 years.
For question (c), you're seeking the regular deposit for a savings annuity with the same interest rate. The formula for a savings annuity is P = A / (((1 + r)^nt - 1) / (r/n)), where P is now the regular deposit needed and A is the future value you want, which is the same as the amount from question (a). Using this formula, you can determine the amount needed to deposit each period.
Finally, for question (d), to find the interest earned with the savings annuity, you would multiply the result from question (c) by the number of periods (20 in this case), and then subtract the future value that you desired from that total to determine the interest earned.