Question

PLZ I need help

Maria has a $5,000 investment with an annual compound interest rate of 15.6%.
After how many years will the initial investment have doubled in value?

Answer 1

5 years to the nearest year.

Explanation:

The formula for Compound Interest with an annual interest payment is

A = P(1 + r/100)^t where A = Amount after t years, P = Initial amount, r = percentage rate.

We have the equation:

10,000 = 5,000(1 + 15.6/ 100)^t

10000 = 5000 * 1.156^t

1.156^t = 2

t ln 1.156 = ln 2

t = ln2 / ln 1.156

t = 4.78

Answer is 5 years.

Answer 2

Answer: it will take 4.8 years

Explanation:

Initial amount invested is $5000. This means that the principal is

P = 5000

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 15.6%. So

r = 15.6/100 = 0.156

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. The amount after t years would be 2 × 5000 = $10000. It means that A = $10000

Therefore

10000 = 5000 (1+0.156/1)^1×t

10000/5000 = (1.156)^t

2 = (1.156)^t

Take log of both sides

log 2 = log (1.156)^t

0.301 = tlog1.156 = 0.063t

t = 0.301/0.063 = 4.8