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Ekonomi Teknik [2] *September 14, 2008*

*Posted by desrinda in Ekonomi Teknik.*

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**TIME VALUE OF MONEY**

– amount and timing

– inflation

– opportunity cost

**INTEREST**

> 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%

**INVESTMENT**

[interest] = [present value] – [original amount]

**LOAN**

[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.

**INTEREST RATE**

**Simple Interest** => calculated independently for each period, more likely to sharia banking operations.

SI = [principal] x [interest rate] x [time]

e.g.

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.

e.g.

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?

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