Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000
immediate up-front payment. The second plan requires you tomake monthly payments of $137.41,
payable at the end of each month for 3 years. What nominal annual interest rate is built into the
monthly payment plan?
You need to set up the problem insuch a way that the cost of the two programs today are equal. At the
end, we are assuming the orthodontist is indifferent between the two plans, taking into consideration
the time value of money.The interest is the value that satisfies the following formula, PV A= PMT
I ×[1− 1
(1+I )N ] .
$ 4,000=$ 137.41
I ×[1− 1
(1+I)36 ]→I=0.011966≈1.2 percent . This is the monthly effective rate.APR=I NOM=12months×1.2 percent
month =0.14359≈14.36 percent
Your sister turned 35 today, and she is planning to save$7,000 per year for retirement, with the first
deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a
return of 7.5% per year. She plans to retire 30years from today, when she turns 65, and she expects to
live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each
year after she retires? Her first withdrawalwill be made at the end of her first retirement year.
You need to equate at t=0 the value of the savings with the value of the retirement income per year. One
way to solve this problem isto get this value at t = 0.
(1+0.075)30 ]+ PMT
(1+0.075)25 ]× 1
Chang Corp. has $375,000 of assets, and it uses only commonequity capital (zero debt). Its sales for
the last year were $595,000, and its net income was $25,000. Stockholders recently voted in a new
management team that has promised to lower costs and...