Question

MATHEMATICS OF BUSINESS AND FINANCE

(a) Lush Gardens Co. bought a new truck for $60,000. It paid $6,000 of this amount as a down payment and financed the balance at 5.19% compounded semi-annually. If the company makes payments of $2,200 at the end of every month, how long will it take to settle the loan?(IN YEARS, MONTHS)

(b) Evan deposits $800 at the end of every 3 months in an RRSP that is earning 5.10% compounded semi-annually. For the RRSP to accumulate to $33,000, calculate the following:

1. How many deposits will he have to make?

2. How long will he have to make these deposits?(in years, months)

Answer 1

a)

Loan Amount (PV)=54000, EAR(Effective Annual Rate)= (1+5.19%/2)^2-1=5.25%,Monthly Rate=5.25%/12=0.438%, PMT=$2200

So, It will take 26 months or 2 year and 2 month tp repay the loan.

b)

EAR=(1+5.1%/2)^2-1=5.165%, 3 month interest= 5.165%/4=1.29%, PMT= 800, FV=33000, PV=0

1. So, He has to make 33 deposits to have $33000

2. It will take 33.28*3=99.84 or 100 month (Approx) or 8 year and 4 month to get $33000.