If a bank account pays 10 % simple interest into an account...

If a bank account pays $10 \%$ simple interest into an account once a year, what is the balance in the account at the end of 8 years if $\$ 1,000$ is deposited into the account at the beginning of each of the 8 years? (Assume there was no balance in the account initially.)

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Key Concepts

Simple Interest

Simple interest is a method of calculating the interest on a principal amount where the interest is computed only on the original amount deposited, rather than on the accumulated balance. This results in a linear increase in the total investment over time since interest on previously earned interest is not taken into account.

Time Value of Money

The time value of money is the concept that money available now is more valuable than the same amount in the future due to its potential earning capacity. This principle underscores that deposits made earlier accrue interest for a longer period, thereby increasing the future value of those deposits relative to later ones.

Multiple Deposits Accumulation

When deposits are made at multiple points in time, each deposit will earn interest for a different duration. This concept involves computing the interest separately for each deposit based on how long it remains in the account and then summing all deposits and their accrued interest to obtain the final balance.

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