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In 2 years, Mia wants to buy a bicycle that costs $600.00. If she opens a savings account that earns 7% interest compounded quarterly, how much will she have to deposit as principal to have enough money in 2 years to buy the bike?

User Fiil
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1 Answer

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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.

User Nitin Jadhav
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