Question 752377: Tanya wants to have $1200 in 2.5 years to go to Mexico.
a)how much money must she invest today at 6.4% annual interest, compounded semi annually to have enough money?
b) Tanya only has $970 today. what interest rate must she obtain to have enough money for her vocation?
c) suppose that Tanya can not find a better rate than 6.4%. what other options does she have?
Answer by josgarithmetic(39631)   (Show Source):
You can put this solution on YOUR website! Question #a: Initial value is $unknown and Tanya wants final value to be $1200.
This is the growth for n compounding periods:
 , where r is the growth rate as a decimal or fraction for the compounding period. A is amount resulting from growth, p is the initial amount invested.
If 6.4% is the yearly rate, then the semi annual rate is HALF of that, or 3.2% for each semi annual period.
and we easily find that 2.5 years to invest is 5 compounding periods.
How you do the rest of the computing is your choice, but with that exponential equation, isolating p is fairly simple.
To the nearest whole dollar, $1025
Question #b:
Here, the question asks for r.
The equation to use would be with values set this way-------
 , but to find the ANNUAL rate instead of this semi-annual based equation, you'll want to multiply r by 2; you will be looking for  .
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