Question

1. Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time.

​$552 per month invested at 5​%, compounded​ monthly, for 3 ​years; then ​$753 per month invested at 7%, compounded​ monthly, for 3 years.

What is the amount in the account after 6 years?

2. Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time.

​$1100 per quarter invested at 6.9​%, compounded​ quarterly, for 12 years; then ​$1600 per quarter invested at 7.7​%, compounded​ quarterly, for 15 years.

Find the final amount in the account.

3. Catherine Dohanyos plans to retire in 20 years. She will make 20 years of monthly contributions to her retirement account. One month after her last​ contribution, she will begin the first of 10 years of withdrawals. She wants to withdraw $3300 per month. How large must her monthly contributions be in order to accomplish her goal if the account earns interest of 7.4​% compounded monthly for the duration of her contributions and the 120 months of​ withdrawals?

The amount of her monthly contributions must be $ _______________  

4.  Find the payment necessary to amortize a 4​% loan of $2400 compounded​ quarterly, with 15 quarterly payments.

The payment size is_____________

Answer 1

1.a. PV= 552, Int=5% p.a. compounded monthly, N=3 years(36), Future Value = 641.13

b. PV= 753, Int=7% p.a. compounded monthly, N=3 years(36), Future Value = 928.39

Amount in the account = 1569.49

2.a. PV= 1100, Int=6.9% p.a. compounded quarterly, N=12 years (48), Future Value = 2499.89

b. PV= 1600, Int=7.7% p.a. compounded quarterly, N=15 years (60), Future Value = 5023.00

Amount in the retirement account = 7522.89

3.a. Annuity=3300 per month, N = 10 years(120), Int. = 7.4%, PV = 279,233.88

b. FV=279,233.88, N = 20 years (240), Int. = 7.4%, PMT = 1721.94 (Monthly)

Catherine has to pay 1721.94 monthly for 20 years in order to meet her target.

4. PV= 2400, Int=4% p.a. compounded quarterly, N=15, Future Value = 2786.32

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