Question

How much will be in your bank account at the end of five years if you invest $10,000 now at 12% per annum, compounded annually? And what if the interest rate is 12% per annum, but compounded monthly?

b) In the poor areas of many cities around the world, we find people offering `pay-day’ loans. One loan agency in Dacca offers to loan Gita $20 till her pay cheque arrives in two weeks time. When it arrives, she must pay back the $20 plus a $2 service charge. What is the effective annual interest rate she is paying on the loan?

c) An oil pipeline is about to be constructed across BC. Some environmentalists are concerned that with the present design, there is a high probability that oil will leak in about 100 years time. If that happens, about 10 billion dollars worth of arable land will be rendered unusable. What is the most it is worth spending now in order to prevent this loss in the future? (Assume that if the money is not spent now, it can be invested at 5% interest.

Answer 1

a. The formula to calculate amount in case of compound interest is

A = P(1+R)^N

Where A is final amount

P is principal invested

R = rate per period

N = number of periods

So here,

A = 10000*( 1+ 0.12)⁵ = 17623.42

i.e A = 17623.42

now, if interest is compounded monthly

R = 12%/12 = 1% per month

N = 5*12 = 60 months

So, A will be

A = 10000*(1 +0.1)⁶⁰ = 18166.97

So, A = 18166.97       

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b.

Same formula as above will be applied

Here A = 20 +2 = $ 22

P = $ 20

N = 2 weeks = 2/52 years = 1/26 years -------- we change this in years as annual interest rate is to be calculated

R = ?

So above formula stands as

22 = 20*(1+R)^1/26

Solving this we will get R as

R = 2.6 or R = 260%

                                                

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c. The same formula for compound interest Amount wiil be used. We have to find P here

10billion = P(1+0.05)¹⁰⁰

Soving this we get

P = 0.076045 billion = 76.045 million

So, the money which can be spent now is $ 76.045 million