Suppose that $7000 is placed in a savings account at an annual rate of 5.6%, compounded semi-annually. Assuming that no withdrawals are made, how long will it take for the account to grow to $8036?

It will take t = 2.5 years for the account to grow to $8036.

Given that,

Total saving amount = $7000

Annual rate = 5.6% = 0.056

We have to determine,

Assuming that no withdrawals are made, how long will it take for the account to grow to $8036.

According to the question,

Amount = $8036

Principal = $7000

Rate = 0.056

n = 2

To find the value of time t calculation done in single unit,

Taking log on both sides,

Hence, It will take t = 2.5 years for the account to grow to $8036.

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2.5 years

Step-by-step explanation:

Amount= $8036

Principal= $7000

Rate =5.6%

t= ?

n= 2

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

8036= 7000(1 + 0.028)^2t

1.148= (1 + 0.028)^2t

log(1.148) = log (1 + 0.028)^2t

0.05994= 2t × 0.01199

t= 2.5 years