Lee Holmes deposited $16,600 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $41,600 at 9% interest compounded semiannually.
At the end of year 6, what is the balance in Lee’s account?
I have tried and I got $44691.78 but that is incorrect. I solved each part separately then added the what he deposited. PLEASE HELP ME!!
It's not quite clear from the language, but it appears that after 3 years, an additional deposit was made, and then the current balance is left to draw 9% interest for two more years. If that's the case, then
to start: 16600
at the end of year 3, he has 16600*1.045^6 = 21617.52
Add 41600 = 63217.52
After two more years, 63217.52*1.045^4 = 75388.07
Oops. That just takes us 5 years.
63217.52*1.045^6 = 82325.66
Make a time graph to see how the periods work
amount = 16600(1.045)^12 + 41600(1.045)^6
= 82 325.65
Thannk you both of you but both answers are incorrect. I can input the answer to see if it is right and both are wrong. We are all missing something. If anyone else wants to try please do!!!
To calculate the balance in Lee's account at the end of year 6, we need to calculate the compounded interest for each deposit separately.
Let's break down the problem step by step:
1. Calculate the interest after the first 3 years on the initial deposit of $16,600.
Since the interest is compounded semiannually, the interest rate for each compounding period is 9% / 2 = 4.5%.
The total number of compounding periods in 3 years is 3 x 2 = 6.
To calculate the interest after each period, we use the formula: A = P(1 + r/n)^(nt), where:
A = the final amount
P = the initial principal
r = the interest rate per period
n = the number of times the interest is compounded per year
t = the total number of years
Using this formula, we can calculate the balance after the first 3 years as:
A = 16,600(1 + 0.045/2)^(2*6) = 16,600(1.0225)^12 = $22,674.55.
2. Calculate the interest after the next 3 years on the additional deposit of $41,600 at the beginning of year 4.
The interest rate and compounding period remain the same, so we can use the same formula again.
The principal amount now becomes $16,600 + $41,600 = $58,200.
The total number of compounding periods is 3 x 2 = 6.
Therefore, the balance after the next 3 years is:
A = 58,200(1 + 0.045/2)^(2*6) = 58,200(1.0225)^12 = $79,610.23.
3. Add the two amounts together to get the total balance at the end of year 6:
Total balance = $22,674.55 + $79,610.23 = $102,284.78.
Therefore, the correct balance in Lee's account at the end of year 6 is $102,284.78.