Question

A saving account earns interest at a rate of 4.8 percent compounded annually. if 100 dollars are initially deposited in this account, no other transactions are made, and interest is paid at the end of the year, what is the least number of years it will take for the value of the account to exceed 300 dollars

explain please

Answer 1

24 years

Explanation:

You want to know the number of years it will take an account's value to exceed $300, given it was opened with $100 and earns 4.8% interest compounded annually.

Account value

The value of the account earning compound interest is ...

A = P(1 +r)^t

where principal P is earning interest at rate r for t years.

Years

Solving for t, we get ...

A/P = (1 +r)^t

log(A/P) = t·log(1+r)

t = log(A/P)/log(1 +r) = log(300/100)/log(1 +0.048)

t = log(3)/log(1.048) ≈ 23.433

For the value to exceed $300, it will take 24 years.

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