Question

Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdrawals, how much will be in the account: How much will be in the account after 25 years using simple interest?

Answer 1

.....................Compound Interest ........................

A.V. = P ( 1 + i ) ⁿ

where :

• A.V. is the Accumulated Value
• P is the Principal Value or Initial Investment
• i is the rate of interest .
• n is the time in years of investment

Given :

P = $ 500

i = 4 % p.a. compound

n = 25 years

Therefore : A.V. = 500 ( 1 + 0.04 ) ²⁵ = 500 ( 1.04 ) ²⁵ = $ 1332.92

.....................Simple Interest ........................

A.V. = P ( 1 + n i )

where :

• A.V. is the Accumulated Value
• P is the Principal Value or Initial Investment
• i is the rate of interest .
• n is the time in years of investment

Given :

P = $ 500

i = 4 % p.a. simple

n = 25 years

Therefore : A.V. = 500 ( 1 + 25 [ 0.04 ] ) = 500 ( 1 + 1 ) = 500 ( 2 )= $ 1000

Hence :

• Accumulated Value using Compound Interest = $ 1332.92
• Accumulated Value using Simple Interest = $ 1000

Compound Interest always leads to accumulated vaue more than or equal to than that using Simple Interest all else being constant .