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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?

Respuesta :

figaroperfect

Answer:

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

Cetacea

Answer: It will take 33.59 years for the balance of this account to reach $8000.

Given:

P=principle=$5000

r=interest rate=1.4%=0.014

A=annuity=$8000

t = Time = ?

n=the number of times compounded yearly=12.

Using the compound interest formula we get:

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\\8000=5000\left(1+\frac{0.014}{12}\right)^{12t}\\1.6=\left(1.00116666667\right)^{12t}\\\ln\left(1.6\right)=\ln\left(1.00116666667\right)^{12t}\\\ln\left(1.6\right)=12t\cdot\ln\left(1.00116666667\right)\\t=\frac{\ln\left(1.6\right)}{12\ln\left(1.00116666667\right)}\\t=33.5912673862\\t=33.59[/tex]

It will take 33.59 years for the balance of this account to reach $8000.

Learn more: https://brainly.com/question/2036104

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