Now, let's find the future value of the annuity.Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period isFV = PMT (1 + i)^¡1The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT = Find the amount accumulated FV in the given annuity account. HINT [See Quick Example 1 and Example 1.] (Assume end-of-period deposits and compounding at the same intervals asdeposits.)Step 1Note that this question asks us to find the amount accumulated in an annuity with an initial investment. To find the future value of the account, we will find the future value of the $15,000and the future value of the monthly deposits separately and then find the sum of the two amounts.Let's begin by finding the future value of the initial $15,000.Recall that the future value FV of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is FV = PV(1 + i)^.Given that $15,000 was the initial investment, PV = 15000$180 deposited monthly for 20 years at 3% per year in an account containing $15,000 at the startIf the annual interest rate of 3% per year as a decimal is 0.03, then the monthly interest rate is i =12Step 2We determined that PV = 15,000, i =If the investment is compounded monthly for 20 years, then the number of periods of compounding is n = 12 · 20 = 240FV ==1500027311.32To find the future value FV, to the nearest cent, substitute the known values into the compound interest formula and proceed to simplify. (Round your final answer to the nearest cent.)FV =PV(1 + i)^15,000 1 +15,00027,311.320.03120.030.03and n = 240. Now, we want to calculate the future value of the initial investment."I1224012Thus, the future value of $15,000 at 3% per year compounded monthly for 20 years is $ 27311.3224027,311.32

Question

Now, let's find the future value of the annuity.Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period isFV = PMT (1 + i)^¡1The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT = Find the amount accumulated FV in the given annuity account. HINT [See Quick Example 1 and Example 1.] (Assume end-of-period deposits and compounding at the same intervals asdeposits.)Step 1Note that this question asks us to find the amount accumulated in an annuity with an initial investment. To find the future value of the account, we will find the future value of the $15,000and the future value of the monthly deposits separately and then find the sum of the two amounts.Let's begin by finding the future value of the initial $15,000.Recall that the future value FV of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is FV = PV(1 + i)^.Given that $15,000 was the initial investment, PV = 15000$180 deposited monthly for 20 years at 3% per year in an account containing $15,000 at the startIf the annual interest rate of 3% per year as a decimal is 0.03, then the monthly interest rate is i =12Step 2We determined that PV = 15,000, i =If the investment is compounded monthly for 20 years, then the number of periods of compounding is n = 12 · 20 = 240FV ==1500027311.32To find the future value FV, to the nearest cent, substitute the known values into the compound interest formula and proceed to simplify. (Round your final answer to the nearest cent.)FV =PV(1 + i)^15,000 1 +15,00027,311.320.03120.030.03and n = 240. Now, we want to calculate the future value of the initial investment.&#34;I1224012Thus, the future value of $15,000 at 3% per year compounded monthly for 20 years is $ 27311.3224027,311.32

Accepted Answer

Answered: Image /qna-images/answer/308c7e3f-7942-4129-9108-be25c393a80f.jpg