Question

Sydney invested $440 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $640?​

Answer 1

Answer:

The time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.

Step-by-step explanation:

Given

• Principle Amount P = $440

• Accrued Amount A = $640

• Interest rate r = 5.6% = 0.056

• Compounded daily n = 365

To determine:

Time period t = ?

Using the formula

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

solving for t

t = ln(A/P) / n[ln(1 + r/n)]

substituting the values A = 640, P = 440, n = 365 and r = 0.056

t = ln(640/440) / ( 365 × [ln(1 + 0.00015342465753425/365)] )

t = 6.691

t ≈ 7  (nearest year)

Therefore, the time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.