Question

Savings Account A has a current balance of $5,200 and earns $18 in interest per month. Savings Account B has a current balance of $4,750 and earns $32 in interest per month. To the nearest month, how many months will it take for Savings A and Savings Account B to have the same balance?
months

Answer 1

To find out how many months it will take for Savings Account A and Savings Account B to have the same balance, we can set up equations based on their current balances and monthly interest earnings.

1. **Account A:**
- Current balance: \( 5200 \)
- Monthly interest: \( 18 \)

After \( t \) months, the balance for Account A will be:
\[
A = 5200 + 18t
\]

2. **Account B:**
- Current balance: \( 4750 \)
- Monthly interest: \( 32 \)

After \( t \) months, the balance for Account B will be:
\[
B = 4750 + 32t
\]

We want to find the number of months \( t \) where both balances are equal:
\[
5200 + 18t = 4750 + 32t
\]

Now, we can solve for \( t \):

1. Rearranging the equation gives:
\[
5200 - 4750 = 32t - 18t
\]
\[
450 = 14t
\]

2. Dividing both sides by 14 gives:
\[
t = \frac{450}{14} \approx 32.14
\]

To the nearest month, it will take approximately \( 32 \) months for both accounts to have the same balance.

Thus, the answer is:
\[
\boxed{32}
\]