Answer:
Final value= $287,663.01
Explanation:
Giving the following information:
If the account balance is less than or equal to $20,000, interest for the next annual period is 7% compounded annually.
If the account balance is greater than $20,000 but less than or equal to $40,000, interest for the next annual period is 10%/year compounded quarterly.
If the account balance is greater than $40,000, interest for the next annual period is 12%/year compounded monthly.
You decide to open an account under these terms today with $11,600.
We need to calculate the time required for the initial investment to reach each limit until the 27 years have passed.
We will use the following formula:
n= ln(FV/PV) / ln(1+i)
<u>First, the number of years to reach $20,000</u>
n= ln(20,000/11,600) / ln(1+0.07)
n= 8.05 years
In the firsts 9 years the account will be invested at a 7% interest rate.
FV= PV*(1+i)^n
FV= 11,600*(1.07)^9
FV= $21,326.13
<u>Now, we need to calculate the number of quarters required to reach $40,000.</u>
i= 0.10/4= 0.025
n= ln(40,000/21,326.13) / ln(1.025)
n= 25.4 quarters
n= 7 years= 28 quarters
FV= 21,326.13*(1.025^28)
FV= $42,577.51
<u>Finally, the 16 years left at a 12% interest rate compounded monthly.</u>
n= 16*12= 192
i= 0.12/12= 0.01
FV= 42,577.51*(1.01^192)
FV= $287,663.01
