Answer:
Mia needs to deposit approximately $522.19 initially in her savings account with a 7% interest rate compounded quarterly to save $600 in 2 years.
Step-by-step explanation:
To calculate how much Mia needs to deposit initially to reach her goal of $600 in 2 years with an interest rate of 7% compounded quarterly, we can use the formula for compound interest, which is:
A = P(1 + r/n)nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested or borrowed for, in years.
In Mia's case:
A = $600 (the future value she wants to have)
r = 0.07 (7% interest rate)
n = 4 (compounded quarterly)
t = 2 (Mia wants to buy the bike in 2 years)
Now we need to rearrange the formula to solve for P:
P = A / (1 + r/n)nt
Substituting the values:
P = $600 / (1 + 0.07/4)4*2
P = $600 / (1 + 0.0175)8
P = $600 / (1.0175)8
P = $600 / (1.148806)
P = $522.19 approximately
Mia needs to deposit approximately $522.19 as principal in her savings account to meet her $600 goal in 2 years with compound interest.