Question

If Mia Wong invests $73,000 at 7 1/2% annual simple interest on March 1, when will her investment be worth $75,760?

Answer 1

Answer:   September 1st

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Work Shown::

1/2 = 0.5

7 & 1/2 = 7 + 1/2 = 7 + 0.5 = 7.5

7.5% = (7.5)/100 = 0.075

She invests P = 73000 dollars at an interest rate of r = 0.075

Let x be some unknown number of years. So t = x.

She wants her investment to be worth $75,760, so this means she wants to earn 75760-73000 = 2760 dollars in simple interest. Let i = 2760

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Apply the simple interest formula to help solve for x

i = P*r*t

2760 = 73000*0.075*x

2760 = 5475x

5475x = 2760

x = 2760/5475

x = 0.5041095890411

This represents the approximate number of years that must elapse for her to get this amount of simple interest.

Let's multiply by 365, since there are 365 days in a year (ignoring leap years) to get

365*0.5041095890411 = 184.000000000001

Due to rounding error, that 1 at the very end likely shouldn't be there. So it looks like exactly 184 days must elapse so that she earns that amount of money.

If she started on March 1, then adding on 184 days leads to September 1.

I recommend looking at a "Day of Year Calendar". Note on this calendar there are numbers for each day. In this case, march 1st occurs on the 60th day of the year while September 1st occurs on the 244th day of the year. Then note how 60+184 = 244. The day of year calendar is a quick way to scroll forward or backward in time on any day. Many online calculators provide an even faster method. The slowest method is to count the number of days on a traditional calendar, but I don't recommend this.