Question

On Juan's 26th birthday, he invested $8,000 in a retirement account. Each year thereafter, he deposited 10% more than the previous deposit. The account paid annual compound interest of 3%.

How much was in the account immediately after his 35th deposit?
Round your answer to the nearest dollar. The tolerance is ± 5.

Answer 1

To find the amount in Juan's account after his 35th deposit, we need to calculate the compound interest for each deposit using the formula. The principal is $8,000, the interest rate is 3%, and the number of periods is 35. Calculating this gives us approximately $6466.

Step-by-step explanation:

To calculate how much is in Juan's account after his 35th deposit, we need to find the amount deposited each year and calculate the compound interest for each deposit. We know that Juan deposited $8,000 on his 26th birthday and each subsequent deposit was 10% more than the previous deposit. So the deposits will follow the pattern:

1. First deposit: $8,000
2. Second deposit: $8,000 + 10% of $8,000
3. Third deposit: $8,000 + 10% more than the second deposit
4. And so on...

To find the amount in the account after the 35th deposit, we can use the formula for compound interest:

Amount = Principal x (1 + Interest Rate)^Number of Periods

In this case, the principal is $8,000 and the interest rate is 3%. The number of periods is 35. Plugging these values into the formula, we get:

Amount = $8,000 x (1 + 0.03)^35

Calculating this gives us approximately $%%6466##