Question

If $7,500 is invested in an account earning 5% interest compounded quarterly, how many years pass until there is $20,000 in the account?
Formula - A=P(1+(r/n))^nt


can someone please help and show me how the answer is found?

Answer 1

If $7,500 is invested in an account earning 5% interest compounded quarterly, how many years pass until there is $20,000 in the account?

**Solution**

$$A = P \left(1 + \frac {r}{n}\right) ^ {n t}$$ $$P = 7500, r = 0.05, n = 4, A = 20000$$

Substitute this values to the equation and solve it for t

$$20000 = 7500 \left(1 + \frac {0.05}{4}\right) ^ {4t}$$ $$\left(1 + \frac {0.05}{4}\right) ^ {4t} = \frac {8}{3}$$ $$1.0125^{4t} = \frac {8}{3}$$ $$t = 19.74 \approx 20$$

**Answer**

20 years