Final answer:
The time it takes to save $25,000 at two different banks with different interest rates and initial deposits is calculated using the compound interest formula. By solving the respective equations for Bank A with 9.35% interest and Bank B with 8.25% interest, we can find the number of years required.
Step-by-step explanation:
To determine how long it will take to save $25,000 for a down payment on a house under each bank's conditions, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the number of years the money is invested for.
For Bank A offering 9.35% interest on an $11,000 deposit, the formula becomes:
$25,000 = $11,000(1 + 0.0935/1)^(1t)
To solve for t, we can rearrange the formula:
t = ln($25,000/$11,000) / ln(1 + 0.0935)
For Bank B offering 8.25% interest on a $10,000 deposit, the formula is:
$25,000 = $10,000(1 + 0.0825/1)^(1t)
Again, solving for t:
t = ln($25,000/$10,000) / ln(1 + 0.0825)
By calculating the above equations, we'll know the number of years required to reach the goal of $25,000 with each bank.