Question

Anna invested $28,000 in an account paying an interest rate of 6.5% compounded daily. 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 $39,500?

Answer 1

Answer:5.3

Explanation:

Answer 2

It will take 5.3 years to reach $39,500

Explanation:

Compound Interest

It occurs when the interest is reinvested rather than paying it out.

Interest in the next compound period is then earned on the principal sum plus the previously accumulated interest.

The formula is:

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

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We are required to find the time needed to convert the principal P into a given final amount.

Solving the above equation for t, we get:

`\displaystyle t=(log(A/P))/(n\cdot log\left(1+r/n\right))`

Anne invested P=$28,000 in an account at r=6.5%=0.065 compounded daily. There are 360 days in a year, so n=360. The final amount A=$39,500.

Substituting into the formula:

`\displaystyle t=(log(39,500/28,000))/(360\cdot log\left(1+0.065/360\right))`

t=5.3 years

It will take 5.3 years to reach $39,500