Trip to Peru algebra question

Question

1. You are planning to go on this trip in 2 years.  How much money will you need to invest at a 2.3% interest rate compounded annually in order to have $2400 in 2 years?  Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)

- Is the answer $220.39?

 

2. Now say you only have $1600 to invest and the highest interest rate you can find is 3.55% compounded annually.  If you decide to wait 7 years to go on the trip, how much money will you have to spend on the trip?  Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)

- Is the answer $64,595,127.42?

Answer 1

1> First of all, look at the answer you have suggested.  Is is reasonable?  $200 can't possible grow to $2400 is 2 years at any reasonable rate of return.  1.023² = 1.046529.  Divide that into 2400 = 2293.30.  Remember the compound interest formula for annual compounding is: A = P(1 + i)ⁿ where P is the amount invested, A is the amount at the end of the term, i is the interest rate and n is the number of years (the term).   Therefore, P, sometimes called the present value of A, is: 

P = A/(1 + i)ⁿ.

 

2> Again look at the answer you have suggested.  Is it reasonable?

If you use the formula noted in the questions (and in the answer to #1):

A = 1600 * (1.0355)⁷ = 1600 * 1.276588 = 2042.54