Question

3) Suppose you deposit $10,000 in a savings account that pays interest at an annual rate of 5%

compounded quarterly. How many years will it take for the balance in your savings account to reach
$12,000?

Answer 1

the answer is 3.67 years

Answer 2

9514 1404 393

Answer:

3.67 years

Explanation:

The amount is found using the compound interest formula.

A = P(1 +r/n)^(nt)

for principal P invested at annual rate r compounded n times per year for t years.

We can solve this for t:

A/P = (1 +r/n)^(nt) . . . . divide by P

log(A/P) = (nt)log(1 +r/n) . . . . take the logarithm

t = log(A/P)/(n·log(1 +r/n)) . . . . divide by the coefficient of t

Filling in the given values, we find ...

t = log(12000/10000)/(4·log(1 +0.05/4)) ≈ 3.6692

It will take about 3.67 years for the balance to reach $12,000.