You want to start a savings account with $240. You want to save up to buy a large screen TV for $399.00. You find an investment opportunity that pays 6% APR interest compounded monthly. How long will it take to turn your initial investment into $399?
A. Write the equation for future value (amount) of a savings account with compound interest compounded multiple times per year. Use the variables A, P, r, n, and t, and explain what each of the variables represent.
B. Write the equation again substituting in the values from the problem above. Make sure that the value that you use for "r" is correct.
C. What is the value of the expression inside the parentheses? If you can give the result that you get to at least 7 to 9 decimal places, unless the result comes out exact or has fewer places.
D. Solve this equation for "t" showing all your work. State your final solution as a decimal value of t to 4 decimal places. (This should be the number of years).
E. Convert this number to years and months. State the number of years and months that you will need in order to save up the money. Round to the nearest whole month.
A=P(1+r/n)^(tn) A = future account value P = present value r/n = decimal interest rate per period where n =number of periods t = time in years tn = number of periods
A = 399 P = 240 r = .06 n = 12 t = the years we are looking for to answer the Q
.06/12 = .005 %
399 = 240 (1+ .005)^12t Divide both sides by 240
1.6625= 1.005^(12t) Take log of bothy sides
.22076 = 12t Log (1.005) Divide both sides by 12
.0183968= t log 1.005 divide both sides by log 1.005
8.4942 years = t
8 ys 5.92 months ~~~ 8 yrs 6 months