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?
Answer: $466 563.74
No, the textbook says Thanh put $5000 into this fund at the BEGINNING of each year
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
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.