Question

If you invest in P dollars and you want the investment to grow to A dollars in t years, the interest rate that must be earned if interest is compounded annually is given by the formula
r =t√A/P-1
If you invest $4000 and want to have $8500 in 8 years, what interest rate must be earned? Round to at least 1 decimal place.

You need an interest rate of at least percent.

Answer 1

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%