Anil invest $ 3500 in an account that pays a rate of 2.4 %per year compound interest.
Find the number of complete years before anil has a least $5000 in this account
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money in the account after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $3500
r = 2.4% = 0.024
A = $5000
We need to find t:
5000 = 3500(1 + 0.024/1)^(1t)
5000 = 3500(1.024)^t
Divide both sides by 3500:
1.4285714 = (1.024)^t
Take the logarithm of both sides to solve for t:
log(1.4285714) = t*log(1.024)
t = log(1.4285714) / log(1.024)
t ≈ 4.71
Anil will have at least $5000 in the account after approximately 4.71 years. Since we cannot have a fraction of a year, Anil will have at least $5000 after 5 complete years.