Answer:
5 years to the nearest year.
Step-by-step 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: it will take 4.8 years
Step-by-step 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
