You want to start a savings account with $250. You want to save up to buy a large screen TV. You find an investment opportunity that pays 4% APR interest compounded monthly. How long will it take to turn your initial investment into $350?
For three points each answer the following questions showing all your work:
Write the equation for future value (amount) of a savings account with compound interest. You may look this up in your notes if you want; you don’t need to have it memorized. Use the variables A, P, r, n, and t, and explain what they each mean.
Write the equation again substituting in the values from the problem above. Be careful to use the correct value for “r”.
What is the value of the expression inside the parentheses? Give your result to at least 7 to 9 decimal places. (I recommend using this much precision when calculating your result below).
Solve this equation for “t” showing all your work. State the solution as a decimal value of t to 4 decimal places. (This is the number of years).
Convert this number to years and months. State the number of years and months it will take to save what you need. Round to the nearest whole month.
Here is a general solution. You translate it into the language they want!!.
FV=PV x [1 + R]^N, where FV=Future value, PV=Present value, R=Interest rate per period, N=Number of periods:
350 = 250 x [1 + 0.04/12]^N
350 = 250 x [1 + 0.003333333333]^N
350 = 250 x 1.003333333333^N Divide both sides by 250
1.4 = 1.003333333333^N Take the log of both sides
N =Log(1.4) / Log(1.003333333333)
N =~101.1099 months, or about 8 years and 5 months.