Yolanda invests $5000 in an account that earns 1.4% annual interest compounded monthly.

How many years will it take for the balance of this account to reach $8000?

33 years, 7 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n) ^ (nt)

where Accrued amount (A) is the expected future balance

A = $8000

P = principal; $5000

r = 1.4% = 0.014

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

8000 = 5000 (1 + 0.014/12) ^ (12t)

Therefore

(1.001167) ^12t = 8000/5000

(1.001167) ^12t = 1.6

finding the log of both sides

12t x log 1.001167 = log 1.6

12t = log 1.6 / log 1.001167

12t = 402.98

t = 402.98/12

t = 33.58

hence time to increase the balance is 33 years, 7 months