Question

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?

Answer 1

The answer is actually 18.7 -.-

Explanation:

Answer 2

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.

Explanation:

We know the formula

`A\:=\:P\left(1\:+\:(r)/(n)\right)^(nt)`

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.