Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdraws or deposits, how many years will it take the account balance to reach at least $6,000?

Question

a. 6 years
b. 7 years
c.10 years
d. 4 years

Answer 1

To solve this problem, we need to use the formula for compound interest:

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

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years

In this case, we have:
P = $5,000
r = 3% = 0.03
A = $6,000

Substituting the values into the formula, we get:

$6,000 = $5,000(1 + 0.03/n)^(n*t)

As we make no other withdraws or deposits, we can assume the interest is compounded annually, which means n = 1.

$6,000 = $5,000(1 + 0.03/1)^(1*t)

Simplifying the equation, we have:

1.2 = (1.03)^t

To solve for t, we can use logarithms:

log(1.2) = log(1.03)^t

0.079181246 = t*log(1.03)

t = 0.079181246 / log(1.03)

Using a calculator, we find:

t ≈ 6.89

Rounding up to the nearest whole number, we get:

t ≈ 7

Therefore, it will take 7 years for the account balance to reach at least $6,000.

The correct answer is b. 7 years.