Question

On january 1st 1960, a person opened a savings account with $100. Interest, at 5% of the amount standing in the account at the time, was added each year on January 1st, starting in 1961. Given that no withdrawals were made, find the year in which there was more than $520 in the account after the interest had been added

Answer 1

1994

Explanation:

After 1 year, the balance has been multiplied by 1.05. After t years, it has been multiplied by 1.05^t.

You want to find t such that ...

100(1.05^t) > 520

1.05^t > 5.20

t×log(1.05) > log(5.20) . . . . take logarithms

t > log(5.20)/log(1.05) ≈ 33.8

The account balance will exceed $520 after interest is added in ...

1960 +34 = 1994