convert interest rate?

Ref: http://www.mathsisfun.com/money/compound-interest-...

1) 5% per annum with semiannual compounding.

So suppose we started with $100. After the first 6 months we will have 100 + (100* (5%)/2) = 102.5

after the next 6 months we will have 102.5 + (102.5 * 5%/2) = 105.0625 or $105.06

2) So the equivalent rate with annual compounding is 5.06%

The general formula is: FV = PV (1+(r/n))^n where

where FV = Future Value

PV = Present Value

r = annual interest rate

n = number of periods of compounding

So in (1) above. PV = 100, r = 5% = 0.05, n =2 ---> FV = 100*(1+0.05/2)^2 = 105.0625

For (2) we have PV = 100, r = ??, n=1 and FV = 105.0625 --> we are solving for r and we get 5.0625%

I think you can do part (b)

For part (c) Continuous Compound Interest Formula is: FV = Pe^(rt)

where, P = principal amount (initial investment)

r = annual interest rate (as a decimal)

t = number of years

FV = amount after time t

e = 2.71828 .....

Interest rate are always quoted ''per annum''

so, 5% every 6 months would be 10% per annum

i.e. A(t) = A(0) x (1.1)^t

Monthly would be 10/12 = 5/6%

i.e. A(t) = A(0) x (1.0083)^12t

Continuous compounding is e^r => e^0.1

i.e. A(t) = A(0) x e^0.1t

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Using the following notation:

r1 = annul rate compounded annually

r2 = annual rate compounded semi annually (r2 = 5% given)

r12 = annual rate compounded monthly

r = compounded continuously

Then the following equations (1 + r1) = (1+r2/2)^2 = (1+r12/12)^12 = e^r

Since r2 = 5%,is given, we get:

r1 = (1.025)^2 - 1 = 0.0506 or 5.06%

r12 = 12[(1.025)^(1/6) -1] = .0495 or 4.95%

r = 2ln(1.025) = .0494 or 4.94 %