Question

Mary would like to save $10 000 at the end of 5 years for a future down payment on a car.
How much should she deposit at the end of each week in a savings account that pays 1.2%/a, compounded monthly, to meet her goal?

If you currently have a part-time job, consider your hourly wage. If you do not have a job, use the minimum hourly wage in your jurisdiction. How many hours each week would you have to work, just to make those payments?

Answer 1

im not sure what grade is this?

Answer 2

grade is this?

Answer 3

hey

Answer 4

hi

Answer 5

For the first part of the question....

I had a similar question yesterday that ate my lunch, but today I got the same answer twice using two different methods, so I am confident my answer/method is correct.

The formula you need is called a sinking fund factor....

A = F { (i) / (/(1+i)^N) - 1) Let me draw it

Answer 6

Solve for A and then you can determine the number of hours Mary would need to work per week at some random wage.

Answer 7

Compounded means you get interest given to you on both the initial amount and the already accumulated interest.. so each compound period, you will multiply your value by the increase rate, it will be an exponential function --
y = A*b^x

(Future value) = (initial value)*(rate of increase)^(times increased)

\[\huge A = P*(1 + \frac{ r }{ n })^{n*t}\]

you want A=10,000
P = Down payment
r = interest rate in decimal
t = time in years
n = how many compounding periods each year

Answer 8

@DanJS I don't see how your equation leads to the answers I got using the sinking fund equation or the TI-84 APPS option 1?

Or is there more info coming?

What is your answer for the amount of her weekly savings?

Answer 9

You take the initial amount P, and multiply it by the percent increase per month

if the annual interest rate is 1.2% = 0.012
the increase per month is 0.012 / 12 , a twelfth of that

so each month you multiply your principal amount by another (1 + 0.012/12)
the exponent is how many times you multiply, here it is once per month for 5 years, 12*5

Answer 10

@DanJS can you plug the values in the formula?

Answer 11

use the minimum hourly wage in your jurisdiction. How many hours each week would you have to work, just to make those payments

Answer 12

Your equation does work if you know P which is the weekly payment saved which I proved by using an Excel spreadsheet. The sinking fund equation calculates A, which is your P, directly. I sure with enough algebra, the sinking fund can be derived from your equation.

FW = P*(1+i / 12)^(N-1)
Time Amount of Payment Future Worth at the of Each Week Number of Payments
1 33.69708 43.65342625 260
2 33.69708 43.60981644 259
3 33.69708 43.56625019 258
4 33.69708 43.52272746 257
.
.
.
257 33.69708 33.79827236 4
258 33.69708 33.76450786 3
259 33.69708 33.73077708 2
260 33.69708 33.69708 1

Sum of all the Weekly Payments $9999.99968

Answer 13

Formatting issues, the Payments on the second line belongs at the end of first line.

Answer 14

so how many hours each week?

Answer 15

how can u solve that using algebra?

Answer 16

First question, How much does Mary make per hour?
Hours = Payment dollars / Wage (dollars/Hour)

Second question, I can't, but there is probably a way. Check out page 37 in the book, "Essentials of Engineering Economics" by James l Riggs copyright @ 1982 McGraw-Hill.

Answer 17

i dont have that book

Answer 18

Library