Question

Your brother has offered to give you $ 175​, starting next​ year, and after that growing at 3.1 % per year for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 6.3 % annual interest rate so long as you have money in the account.

a. How much money will you need to deposit into the account​ today?

b. Assuming you deposited the amount of money in part ​(a​), and then withdrew the required payments each​ year, calculate the remaining balance at the end of years​ 1, 2, 10 and 19.​ (Hint: To solve this problem it is best to use an excel​ spreadsheet.) Please round these numbers to the nearest cent

Your brother has offered to give you $ 175​, starting next​ year, and after that growing at 3.1 % per year for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 6.3 % annual interest rate so long as you have money in the account.

a. How much money will you need to deposit into the account​ today?

b. Assuming you deposited the amount of money in part ​(a​), and then withdrew the required payments each​ year, calculate the remaining balance at the end of years​ 1, 2, 10 and 19.​ (Hint: To solve this problem it is best to use an excel​ spreadsheet.) Please round these numbers to the nearest cent

Answer 1

(a) Annual Withdrawal = $ 175, Interest Rate = 6.3 % and Withdrawal Tenure = 20 years, Deposit Growth Rate = 3.1%

Amount Required to be Deposited at Present = Total Present Value of Annual Withdrawals = 175 / (0.063-0.031) x [1-{(1.031)/(1.063)}^(20)}] = $ 2501.21

(b)