Question

Michelle is attending college and has a​ part-time job. once she finishes​ college, michelle would like to relocate to a metropolitan area. she wants to build her savings so that she will have a​ "nest egg" to start her off. michelle works out her budget and decides she can afford to set aside ​$130130 per month for savings. her bank will pay her 5 %5% per​ year, compounded​ monthly, on her savings account. what will be​ michelle's balance in five​ years?

Answer 1

To calculate Michelle's balance in five years with compound interest, use the formula A = P(1 + r/n)^(nt). Plugging in the values, the balance is approximately $7,403.69.

Step-by-step explanation:

To calculate Michelle's balance in five years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount (balance) in the account
• P is the initial amount (monthly savings)
• r is the annual interest rate (5% or 0.05 in decimal form)
• n is the number of times interest is compounded per year (12 for monthly compounding)
• t is the number of years

Plugging in the values from the question:

• P = $130
• r = 0.05
• n = 12
• t = 5

we can solve for A:

A = 130(1 + 0.05/12)^(12*5)

Calculating this expression gives us a balance of approximately $7,403.69. So, Michelle's balance after five years will be $7,403.69.

Answer 2

$8877.62 This is an example of an investment with compound interest and regular contributions each period. So let's examine it closely. To make things easier, I'll work with individual months instead of entire years. So we'll have 60 periods (12 * 5) and the interest rate for each period will be 5/12 = 0.41666%. For the interest, we'll add 1 and call the value z, so that our math doesn't have to keep adding. The contribution each month will be called C which will be made at the beginning of the month. So let's look at the end of the first few months. 1. Cz 2. Cz^2 + Cz = C(z+ z^2) 3. Cz^3 + Cz^2 + Cz = C(z + z^2 + z^3) ... n. Cz^n + Cz^(n-1) + ... + Cz = C(z + z^2 + ... + z^n) The (z + z^2 + ... + z^n) part is the sum of a geometric series. If you look it up, you'll see that it reduces to this (z^(n+1) - z)/(z-1) Now we can calculate how much Michelle will have after 60 months. T = 130(z^61 - z)/(z-1) z = 1 + 0.05/12 = 1.004166667 so T = 130(1.004166667^61 - 1.004166667)/(1.004166667-1) T = 130(1.288706006 - 1.004166667)/.004166667 T = 130(0.28453934)/.004166667 T = 130(68.28944152) T = 8877.627398 So Michelle will have after 5 years, $8877.62 saved.