Question

Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 5.5% if the money is a) compounded semiannuallyb) compounded quarterlyc) compounded monthlyd) compounded continuously

Answer 1

Apply the compound interest formula:

A = P (1+ r/n)^nt

Where:

A = Value of the investment after interests

P = principal investment

r= interest rate (in decimal form ) =5.5/100 = 0.055

t= years

n= number of compounding periods in each year

Replacing:

A = 10,000 (1+0.055/n)^5n

• a) n=2

A = 10,000 (1+0.055/2)^(5x2)

A = 10,000( 1+0.0275)^10

A = 10,000 ( 1.0275)^10

A = $13,116.5

• b) n=4

A = 10,000 (1+0.055/4)^(5x4)

A = 10,000 (1.01375)^20

A = $13,140.66

• C) n=12

A = 10,000 (1+0.055/12)^(5x12)

A = 10,000 (1.004583333)^60

A= $13,157.03

• d) for compounded continuously apply:

,

•

A = P x e ^(rt)

where

e ≅2.7183

A = 10,000 x 2.7183 (0.055 x5) = $13,165.33