A superannuation fund paid 6% p.a. for the first 10 years and then 10% p.a. after that. If Thanh put $5000 into this fund at the end of each year, how much would she have at the end of 25 years?

amount after 10 years

= 5000( 1.06^10 - 1)/.06 = 65,903.40
let this side for 15 years at 10%
= 65903.40(1.1)^15 = 275,297.26

consider a 2nd annuity of 5000 for 15 years at 10%
= 5000( 1.10^15 - 1)/.10 = 158,862.41

for a total of 275,297.26 + 158,862.41 = $341,201.23

how did you get $466 563.74

I never got $466 563.74. The answers in the textbook I use said that

No, the textbook says Thanh put $5000 into this fund at the BEGINNING of each year

To calculate the final amount in Thanh's superannuation fund at the end of 25 years, we can break down the problem into two parts: calculating the accumulated amounts for the initial 10 years at the interest rate of 6% p.a. and then calculating the accumulated amounts for the remaining 15 years at the interest rate of 10% p.a.

1. Calculation for the first 10 years:
To determine the accumulated amount for the initial 10 years, we need to calculate the future value of these yearly investments at an interest rate of 6% p.a.
We can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r) ^ n - 1] / r

Where:
FV = Future Value (accumulated amount)
P = Yearly investment amount ($5000)
r = Rate of interest per compounding period (6% p.a. or 0.06)
n = Number of compounding periods (10 years)

Using the above formula, we can calculate the accumulated amount for the initial 10 years:

FV1 = 5000 * [(1 + 0.06) ^ 10 - 1] / 0.06
FV1 ≈ $67,306.20

2. Calculation for the next 15 years:
To determine the accumulated amount for the remaining 15 years, we need to calculate the future value of these yearly investments at an interest rate of 10% p.a.
Using the same formula as above, with the adjusted values:

P = Yearly investment amount ($5000)
r = Rate of interest per compounding period (10% p.a. or 0.10)
n = Number of compounding periods (15 years)

FV2 = 5000 * [(1 + 0.10) ^ 15 - 1] / 0.10
FV2 ≈ $399,257.54

3. Total accumulated amount after 25 years:
To calculate the total accumulated amount, we need to add the amounts calculated for the first 10 years and the next 15 years:

Total FV = FV1 + FV2
Total FV ≈ $67,306.20 + $399,257.54
Total FV ≈ $466,563.74

Therefore, Thanh would have approximately $466,563.74 in her superannuation fund at the end of 25 years.