Sarah invested $1000 in an account paying 5.5% interest compounded semi-annually. How long will it take for the account balance to reach $10,450?

Answer: it will take 43.25 years

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,

P = $1000

A = $10450

r = 5.5% = 5.5/100 = 0.055

n = 2 because it was compounded 2 times in a year.

Therefore,.

10450 = 1000 (1 + 0.055/2) ^2 * t

10450/1000 = (1 + 0.0275) ^2t

10.45 = (1.0275) ^2t

Taking log of both sides, it becomes

Log 10.45 = 2t log 1.0275

1.019 = 2t * 0.01178 = 0.02356t

t = 1.019/0.02356

t = 43.25 years