Question

1. Larry can make monthly payments of $ 221.00 a month to buy a truck. If the dealer offers a 4 year, 3.0% interest loan, about what is the most expensive truck can Larry buy?

2. You have $200,000 in your retirement account. You want to withdraw $13,000 a year for 30 years. How much must your retirement account earn for you to obtain your goal?

3. The discount rate is 5.46%. What is the most you would pay for the following payments: $ 10,000 in two years; $20,000 in four years; $ 25,000 in five years?

Answer 1

1)
Monthly Payment, PMT = 221
No. of Payment, n = 4*12 = 48 Months
Interest Loan,i = 3% per annum = 3%/12 = 0.0025 per month

Present Value = PMT/i * [1-(1+i)^-n]
Present Value = 221/0.0025 * [1-(1+0.0025)^-48]
Present Value = 88400 * [1-0.8871]
Present Value = 88400 * 0.1129
Present Value = $ 9984

2) Present Value, PV = 200,000
Annual Withdrawl, PMT = 13,000
Period, n = 30 Years

Present Value = PMT/i * [1-(1+i)^-n]

200000 = 13000/i * [1-(1+i)^-30]
This can be solved either using financial calculator or excel. Here I am refering excel

Use Excel Formula "=RATE(n,-PMT,PV)"
Use Excel Formula "=RATE(30,-13000,20000)"

This will Give Interest Rate = 5%

Retirement account should earn 5% to obtain your goal

3)
Payment now for Future Receipts = Present Value of Future Payments at 5.46%
Payment now for Future Receipts = 10000/(1+5.46%)² + 20000/(1+5.46%)⁴ + 25000/(1+5.46%)⁵
Payment now for Future Receipts = 10000/1.1122 + 20000/1.2369 + 25000/1.3045
Payment now for Future Receipts = 8991+16169+19165
Payment now for Future Receipts = 44325