Question 1202635: Ali invests $14 800 in an account that earns interest compounded semi-annually for 8 years. She then takes all the money, which amounts to $17 063.24, and invests it in an account that earns interest compounded quarterly for 6 years. After the 14 years, the account is worth $18 846.11. What annual interest rate was Ali earning on each of the accounts?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Compound interest formula
A = P*(1+r/n)^(n*t)
A = final amount
P = deposit
r = annual interest rate in decimal form
n = compounding frequency
t = number of years
Use this given info
"Ali invests $14,800 in an account that earns interest compounded semi-annually for 8 years...which amounts to $17,063.24"
to determine:
A = 17063.24
P = 14800
r = unknown
n = 2
t = 8
A = P*(1+r/n)^(n*t)
17063.24 = 14800*(1+r/2)^(2*8)
17063.24 = 14800*(1+r/2)^16
17063.24/14800 = (1+r/2)^16
1.15292162 = (1+r/2)^16
(1+r/2)^16 = 1.15292162
1+r/2 = (1.15292162)^(1/16)
1+r/2 = 1.00893337
r/2 = 1.00893337-1
r/2 = 0.00893337
r = 2*0.00893337
r = 0.01786674
r = 0.01787
The first account has an annual rate of about 1.787%
For the 2nd account, Ali has:
A = 18846.11
P = 17063.24
r = unknown
n = 4
t = 6
Caution: The instructions mention After the 14 years, but we will not use t = 14 for the 2nd account.
The money sits in the 2nd account for 6 years and not 14.
The 14 refers to 8 years + 6 years = 14 years total.
I'll skip the steps (since they will be similar to the ones shown above), but you should get r = 0.0166 to represent an annual rate of approximately 1.66%
|
|
|
