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History Bookmarks Develop Window Help sfu.ca www.sfu.ca/-bick/bus316/RETO9-RET10.Pr.pdf www.sfu.ca/-bick/bus 316/POS24.Pr.pdf Copy Student number:. Class Problem RET-9 Suppose you invest $500,000 For a period of The interest rate is r Compute the maturity value of the loan (be exact to within $.01) under each one of the following assumptions: (a) ris a simple rate per 360 days. (b) ris a simple rate per 365 days. (c) ris a daily-compounded rate (using a 365 day year). (d) r is a continuously-compounded rate (using a 365 day year). (e) r is an effective annual rate (using a 365 day year). 175 days 0.05 5.00% pa. = (This is completed for you.) Maturity value 512.152.78

Explanation / Answer

a.

Formula for simple interest:

A = P x (1+rt)

A = Maturity amount

P = Principal amount = $ 500,000

r = Rate of interest per year = 5 %

t = Time in years = 175/360

A = $ 500,000 x (1+ 5% x 175/360)

    = $ 500,000 + $ 500,000 x 0.05 x 0.486111111

    = $ 500,000 + 12,152.78 = $ 512,152.78

b.

Using same formula for simple interest,

A = $ 500,000 x (1+ 5% x 175/365)

    = $ 500,000 + $ 500,000 x 0.05 x 0.479452055

    = $ 500,000 + 11,986.30 = $ 511,986.30

c.

Formula for compound interest:

A = P x (1 + r/m) mt

A = Future value of investment

P = Principal = $ 500,000

r = Rate of interest = 5 % p.a.

m = No. of compounding in a year = 365

t = No. of periods = 175

A = $ 500,000 x (1+0.05/365)175

= $ 500,000 x (1+0.000136986)175

= $ 500,000 x (1.000136986)175

  = $ 500,000 x 1.024260574

= $ 512,130.29

d.

Formula for continuous compounding:

A = P x e rt

A = Amount after maturity

P = Principal = $ 500,000

e = 2.71828

r = Rate of interest = 5 % p.a.

t = Time in years = 175/365

A = $ 500,000 x 2.71828 0.05 x 175/365

   = $ 500,000 x 2.71828 0.023972603

   = $ 500,000 x 1.024262239

   = $ 512,131.12

e.

r = (1+i/n) n – 1        

r = Effective annual interest rate

i = Stated annual interest rate = 0.05

n = No. of compounding periods in a year = 365

[Assumed to be daily as not mentioned compounding frequency]

r = (1+0.05/365)365 – 1

   = (1 + 0.000136986)365 – 1

   = (1.000136986)365 – 1

   = 1.051267496 – 1 = 0.051267496

A = $ 500,000 x (1+0.051267496/365)175

= $ 500,000 x (1+0.000140459)175

= $ 500,000 x (1.000140459)175

  = $ 500,000 x (1.024260574)175

= $ 500,000 x $ 1.024883124

= $ 512,441.56

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