Suppose Taylor win $18000 in a lottery. If she invests half in a CD earning 4.2 % annual interest compounded quarterly and the rest in saving account earning 3.7% annual interest compounded monthly . How much money does she have after 10 years
amount = 9000(1.0105)^40 + 9000(1.00308333...)^120
=
To calculate the amount of money Taylor will have after 10 years, we can divide the problem into two parts:
1. Calculate the interest accumulated on the amount invested in the CD.
2. Calculate the interest accumulated on the amount invested in the savings account.
Let's break down these calculations:
1. Amount invested in the CD: $18000/2 = $9000
The CD earns 4.2% annual interest, compounded quarterly. The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $9000
r = 4.2% or 0.042 (converted to decimal)
n = 4 (interest is compounded quarterly)
t = 10 years
Using the formula, we can calculate the amount accumulated in the CD after 10 years:
A_cd = $9000(1 + 0.042/4)^(4*10)
2. Amount invested in the savings account: $18000/2 = $9000
The savings account earns 3.7% annual interest, compounded monthly. Applying the same formula as above:
P = $9000
r = 3.7% or 0.037 (converted to decimal)
n = 12 (interest is compounded monthly)
t = 10 years
Using the formula, we can calculate the amount accumulated in the savings account after 10 years:
A_savings = $9000(1 + 0.037/12)^(12*10)
Now, we can calculate the total amount of money Taylor will have after 10 years:
Total = A_cd + A_savings
Simply substitute the calculated values and solve the equation to find the final amount.