Joshua plans to retire in 25 years. He will make 15 years of equal monthly payments into his account. Ten years after his last contribution, he will begin the first of 120 (10 years) of withdrawals of $2900 per month. Assume that the retirement account earns interest of 5.4% compounded monthly for the duration of his contributions, the 10 years in between his contributions and the withdrawals, and the 10 years of withdrawals. How large must Joshua's monthly contributions be in order to accomplish his goal? (The parts below will help you work through this problem.) (a) If Joshua wants to fund 10 years of monthly withdrawals of $2900 at 5.4% interest, compounded monthly, how much needs to be in the account? (b) Use your answer from part (b) as future value to find the present value of a compound interest account for the intervening 10 years. (e) This gives you the amount in the account at the end of the 15 years of payments into the account. Use this information to solve for PMT. Problem adapted from Mathematics with Applications Suppose that you take out a $1000 loan at 3.1% interest, compounded monthly. You will make monthly payments at the end of each of the next 4 months to repay the loan. (a) Find the monthly payment for the loan. (b) Complete the following amortization table. Month Amount of Payment | Interest for Period Amount to Principal | Principal Remaining 0 1 2 3 4 $1000
Joshua plans to retire in 25 years. He will make 15 years of equal monthly payments into his account. Ten years after his last contribution, he will begin the first of 120 (10 years) of withdrawals of $2900 per month. Assume that the retirement account earns interest of 5.4% compounded monthly for the duration of his contributions, the 10 years in between his contributions and the withdrawals, and the 10 years of withdrawals. How large must Joshua's monthly contributions be in order to accomplish his goal? (The parts below will help you work through this problem.) (a) If Joshua wants to fund 10 years of monthly withdrawals of $2900 at 5.4% interest, compounded monthly, how much needs to be in the account? (b) Use your answer from part (b) as future value to find the present value of a compound interest account for the intervening 10 years. (e) This gives you the amount in the account at the end of the 15 years of payments into the account. Use this information to solve for PMT. Problem adapted from Mathematics with Applications Suppose that you take out a $1000 loan at 3.1% interest, compounded monthly. You will make monthly payments at the end of each of the next 4 months to repay the loan. (a) Find the monthly payment for the loan. (b) Complete the following amortization table. Month Amount of Payment | Interest for Period Amount to Principal | Principal Remaining 0 1 2 3 4 $1000
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 23P
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Transcribed Image Text:Additionally complete the following problems (showing all work):
i. Joshua plans to retire in 25 years. He will make 15 years of equal monthly payments into his account.
Ten years after his last contribution, he will begin the first of 120 (10 years) of withdrawals of $2900
per month. Assume that the retirement account earns interest of 5.4% compounded monthly for the
duration of his contributions, the 10 years in between his contributions and the withdrawals, and the
10 years of withdrawals. How large must Joshua's monthly contributions be in order to accomplish
his goal? (The parts below will help you work through this problem.)
(a) If Joshua wants to fund 10 years of monthly withdrawals of $2900 at 5.4% interest, compounded
monthly, how much needs to be in the account?
(b) Use your answer from part (b) as future value to find the present value of a compound interest
account for the intervening 10 years.
(c) This gives you the amount in the account at the end of the 15 years of payments into the
account. Use this information to solve for PMT.
Problem adapted from Mathematics with Applications
ii.
1. Suppose that you take out a $1000 loan at 3.1% interest, compounded monthly. You will make
monthly payments at the end of each of the next 4 months to repay the loan.
(a) Find the monthly payment for the loan.
(b) Complete the following amortization table.
Month | Amount of Payment | Interest for Period Amount to Principal Principal Remaining
$1000
0
1
2
3
4
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