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Aubree invested $4,400 in an account paying an interest rate of 2.4% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest tenth of a year, for the value of the account to reach $6,880?

Sagot :

absor201

Answer:

We conclude that the time required to get  a total amount of $6,880.00  from compound interest on a principal of $ 4,400.00  at an interest rate of 2.4% per year  and compounded 4 times per year  is 18 years and 8 months.

Step-by-step explanation:

We know the formula

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

where

  • A denotes the Accrued Amount (principal + interest)
  • P denotes the Principal Amount
  • r denoted the Annual Interest Rate
  • t denotes the Time Period in years
  • n denotes the number of compounding periods per unit t

Given

Total amount A = $6,880

Principle amount P = $4,400

Interest Rate r =  2.4% = 0.024 per year

Compounded quarterly = n = 4

Thus, the time period can be fetched using  the simplified-derived equation suchs as:

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

substituting the values

t = ln(6,880.00/4,400.00) / ( 4 × [ln(1 + 0.006/4)] )

t = 18.8 years

Therefore, we conclude that the time required to get  a total amount of $6,880.00  from compound interest on a principal of $ 4,400.00  at an interest rate of 2.4% per year  and compounded 4 times per year  is 18 years and 8 months.

jarrattjett

Answer:

The answer is actually 18.7 -.-

Step-by-step explanation:

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