Answer: You need an interest rate of at least 9.9%
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
A = $8500
P = $4000
n = 1 because it was compounded once in a year.
t = 8 years
Therefore,
8500 = 4000(1 + r/1)^1 × 8
8500/4000 = (1 + r)^8
2.125 = (1 + r)^8
Taking log of both sides of the equation, it becomes
Log 2.125 = 8 log (1 + r)
0.327 = 8 log (1 + r)
0.327/8 = 8 log (1 + r)
0.040875 = log (1 + r)
Taking inverse log of both sides of the equation, it becomes
10^0.040875 = 10^log (1 + r)
1.099 = 1 + r
r = 1.099 - 1
r = 0.099
r = 0.099 × 100 = 9.9%
