Ekonomi Teknik  September 14, 2008Posted by desrinda in Ekonomi Teknik.
TIME VALUE OF MONEY
– amount and timing
– opportunity cost
> manifestation of time value of money
> the amount paid to use money
> rental fee paid for the use of other’s money, expressed as A%
[interest] = [present value] – [original amount]
[interest] = [total owed now] – [original amount]
CASH FLOW DIAGRAM
Engineering Economy had developed a graphical technique for presenting a problem dealing with cash flows and their timing.
Simple Interest => calculated independently for each period, more likely to sharia banking operations.
SI = [principal] x [interest rate] x [time]
Borrow USD 1,000 for 3 years at rate 5% per year.
SI = USD 1,000 x 0.05 x 3 = USD 150 paid at the 3rd year, total = USD 1,150
Compound Interest => calculated for each period and added to the principal amount.
Borrow USD 1,000 at rate 5% per year.
First year = USD 1,000 + (USD 1,000 x 0.05) = USD 1,050
Second year = USD 1,050 + (USD 1,050 x 0.05) = USD 1,102.50
Thirs year = USD 1,102.50 + (USD 1,102.50 x 0.05) = USD 1,157.625
ASSIGNMENT I (to be submitted on September 20, 2008)
1. Supposed you wanted to be a millionaire at retirement. If an annual compound interest rate of 8% can be sustained over a 40 years period, how much you have to deposit yearly to accumulate $ 1 million?
2. If a fund pays 10% compounded annually, what single deposit now will accumulate $ 12,000 at the end of the tenth year? If the fund pays 5% instead of 10%, how much to deposit to end up with $ 6,000?
3. What equal annual deposits must be made at t = 2, 3, 4, 5 and 6 in order to accumulate $ 15,000 at t = 8 if money is worth 10% compounded annually?
4. Dede borrows $ 15,000 at 15% compounded annually; he pays off the loan over 5 – year period with annual payments. Each successive payment is $ 500 less than the previous one. How much was his first payment?
5. Bono wishes to make a single deposit P at t = 0 into a fund giving 12% compounded quarterly such that $ 1,000 payments are received at t = 1, 2, 3, and 4 (periods are 3 month intervals), and a single payment of $ 7,500 is received at t = 12. What single deposit is needed?