We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $6,000)
P = the principal amount (in this case, $5,000)
r = the annual interest rate (3%)
n = the number of times the interest is compounded per year (we'll assume it's compounded annually, so n = 1)
t = the number of years
Plugging in the values we know, we get:
6,000 = 5,000(1 + 0.03/1)^(1t)
Simplifying:
1.2 = (1.03)^t
Taking the natural logarithm of both sides:
ln(1.2) = t ln(1.03)
Dividing both sides by ln(1.03):
t = ln(1.2) / ln(1.03) ≈ 7.22
So it will take about 7 years for the account balance to reach at least $6,000. The answer is c) 7 years.
Suppose you deposit $5,000 in savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000?
a) 10 years
b) 6 years
c) 7 years
d) 4 years
1 answer
1 answer