Suppose that on September 30, 2021, a person opened an investment account with an initial deposit of $20,000. The account guarantees to pay interest at a nominal annual rate of 6%, compounded monthly. The person plans to deposit $3,000 into the account at the end of each and every month starting on October 31, 2021 and ending on March 31, 2024 (a total of 30 additional deposits). (a) How much money will be in the account after the 30th additional deposit is made? (b) What is the total amount of interest that will be earned over the 30-month planning horizon? (c) What is the effective annual interest rate that will be earned? Express your answer to the nearest tenth of a percent, i.e., in the form xx.x%.
Suppose that on September 30, 2021, a person opened an investment account with an initial deposit of $20,000. The account guarantees to pay interest at a nominal annual rate of 6%, compounded monthly. The person plans to deposit $3,000 into the account at the end of each and every month starting on October 31, 2021 and ending on March 31, 2024 (a total of 30 additional deposits).
(a) How much money will be in the account after the 30th additional deposit is made?
(b) What is the total amount of interest that will be earned over the 30-month planning horizon?
(c) What is the effective annual interest rate that will be earned? Express your answer to the nearest tenth of a percent, i.e., in the form xx.x%.
PV = Amount of Deposit = $20,000
P = Monthly Deposit = $3,000
n = 30 months
r = Monthly Interest rate = 6%/12 = 0.05%
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