Superannuation Question (1 Viewer)

[Schniz]

An insurance company offers 10% p.a. compound intereson inverstments in its superannuation fund. If a contributor pays in $P at the beginning of each year, show that after "n" years his superannuation entitlement is $11P[(1.1^n)-1]

 

[word.]

An insurance company offers 10% p.a. compound intereson inverstments in its superannuation fund. If a contributor pays in $P at the beginning of each year, show that after "n" years his superannuation entitlement is $11P[(1.1^n)-1]

Year 1: P * 1.1
Year 2: (Year 1 + P) * 1.1 = (P * 1.1 + P) * 1.1 = 1.1(1.1P + P)
Year 3: (Year 2 + P) * 1.1 = 1.1 * [P(1.1)² + P(1.1) + P]
Year n: = 1.1 * [P(1.1)^(n-1) + P(1.1)^(n-2) + ... + P(1.1) + P]

Consider the expression within the square brackets; this is a geometric progression where: a = P, r = 1.1, n = n.
Sn = P(1.1ⁿ - 1)/0.1 = 10P(1.1ⁿ - 1)

Year n = 1.1 * 10P(1.1ⁿ - 1) = 11P(1.1ⁿ - 1)

Hence after "n" years his superannuation entitlement is $11P[(1.1ⁿ) - 1] #

 

[Schniz]

thanks