calculating the periodic payment, number of payments, and interest rate参考.ppt

Chapter 13 Annuities Due 13.3 calculating the periodic payment, number of payments, and interest rate Example A lease that has years to run is recorded on a company’s books as a liability of $27,369. If the company’s cost of borrowing was 12% compounded monthly when the lease was signed, what is the lease payment at the beginning of each month? PV(due)=$27,369 term=2 1/2 years n=30 j=12% compounded monthly p=i=j/m=1% Example Mr. Walters has already accumulated $104,000 in his Registered Retirement Savings Plan (RRSP). His goal is to build it to $250,000 with equal contributions at the beginning of each 6-month period for the next 7 years. If his RRSP earns 8.5% compounded semiannually, what must be the size of further contributions? Algebraic method: Step 1: calculate FV(due) j=8.5% compounded semiannually i=j/m=4.25% term=7 years n=7*12/6=14 Step 2: calculate S Step 3: FV(due)+ S=$250,000 R=$3286.10 Financial calculator method Example R=$2000 PV(due)=$210,000 j=9% compounded semiannually i=j/m=4.5% per half year * * The mathematics of vehicle leasing The main elements of a typical lease contract are as follow: 1, the payments are made at the beginning of the payment interval. And most common term of the lease is three years. 2, the lessee is responsible for all vehicle operating cost including the insurance during the term of the lease. 3, At the end of the term, the lessee can simply return the vehicle to the car dealer. Alternatively the vehicle can be purchased for the residual value which is the estimation of the market value of the vehicle at the end of the lease. 4, the interest rate on leases is a monthly compounded rate----the lease payments form a simple annuity due. present value of the residual value Purchase price down payment - = + present value of the lease payments Solution: Algebraic method Financial calculator method FV PV n 1/y PMT 30 1 0 27369 -1050 BGN CPT Sol