Math help for a question based on annuities (sequence and series)

[Mandynguyennmm]

Hi
can i please have help for this question:
How much superannuation will there be at the end of 18 years if $690 is invested at 8.5% p.a. at the beginning of each year?

my working out:
n=18
P= 690
r=0.0895

A= 690 x 1.0895^18 + 690 x 1.0895^17 + 690 x 1.0895^16 +..........+690 x 1.0895^2 + 690 x 1.0895
A= 690 x 1.0895 ( 1 + 1.0985 + 1.0895^2 +......+1.0895^17)
A= 690 x 1.0895 [(1.0895^18-1)/(1.0895-1)]
A=$30896.07

but the answer is meant to be $29 439.16


thanks

[RuiAce]

Hi
can i please have help for this question:
How much superannuation will there be at the end of 18 years if $690 is invested at 8.5% p.a. at the beginning of each year?

my working out:
n=18
P= 690
r=0.0895

A= 690 x 1.0895^18 + 690 x 1.0895^17 + 690 x 1.0895^16 +..........+690 x 1.0895^2 + 690 x 1.0895
A= 690 x 1.0895 ( 1 + 1.0985 + 1.0895^2 +......+1.0895^17)
A= 690 x 1.0895 [(1.0895^18-1)/(1.0895-1)]
A=$30896.07

but the answer is meant to be $29 439.16


thanks

Your method is correct. It's just that for some reason you wrote r = 0.0895 instead of r = 0.085

[Mandynguyennmm]

oh, thank you.

also lastly can i have help for this question:
 A sum of $1500 is invested at the end of each year for 15 years at 8% p.a. Find the amount of superannuation available at the end of the 15 years.
Answer= $40 728.17

my method:
P=1500
n=15
r=0.08

A=1500 x 1.08^15 + 1500 x 1.08^14 + 1500 x 1.08^13 +.......+1500 x 1.08^2 + 1500 x 1.08
A= 1500 x 1.08 (1 + 1.08 + 1.08^2 +.....+1.08^14)
A= 1500 x 1.08 [ (1.08^15-1)/(1.08-1) ]
A=$43986.42

[RuiAce]

oh, thank you.

also lastly can i have help for this question:
 A sum of $1500 is invested at the end of each year for 15 years at 8% p.a. Find the amount of superannuation available at the end of the 15 years.
Answer= $40 728.17

my method:
P=1500
n=15
r=0.08

A=1500 x 1.08^15 + 1500 x 1.08^14 + 1500 x 1.08^13 +.......+1500 x 1.08^2 + 1500 x 1.08
A= 1500 x 1.08 (1 + 1.08 + 1.08^2 +.....+1.08^14)
A= 1500 x 1.08 [ (1.08^15-1)/(1.08-1) ]
A=$43986.42

You assumed that you're investing at the beginning of each year.

When you invest at the beginning of each year, the investment earns interest that same year, which is why we have the extra 1.08. When you invest at the end of each year, you don't have that extra interest factor anymore.

The correct answer is \(A = 1500\times 1.08^{14} + 1500\times 1.08^{13} + \dots + 1500\times 1.08 + 1500\)

[Mandynguyennmm]

yes okay, thanks for the help