Question

Mario decided to invest his $620 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. Answer the following questions, assuming that Mario deposits his entire refund and does not deposit or withdraw any other amounts.

a. Write an equation that models the growth of the investment.
b. How many years will it take for the initial investment to double?

Answer 1

The Compound Interest formula is: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]
Here, P = Principal = $620
r = 4% (express it in decimal) = 0.04
n = compounding period = 4 (because it is quarterly, it is compounded 4 times a year)
Plug in the numbers and simplify if possible and that will be your part a)

For part b) Put in A = 620 * 2 (doubling the investment) and solve for t

Answer 2

Figure out the compounded interest rate first.
rate = (1 + r/n)^n where n is the number of compounding periods.
rate = (1 + .04/4)^4
rate = 1.0406040

So for part a the equation is
total = princ * (1.040604)^n (number of years)

Answer 3

Now for part b
We need to calculate when the amount is $1,240

1,240 = 620 * (1.040604)^n
1,240 / 620 = (1.040604)^n
We have to solve for n (years)
Taking logs of both sides:
log (1,240) -log (620) = years * log (1.040604)
years = (log (1,240) - log (620)) / log (1.040604)
years = 0.3010299957 / 0.0172854951
years = 17.4151792234

Answer 4

Ok thanks you guys so much

Answer 5

u r welcome