saved $ 5000 in a saving account which pays 12% interest compounded monthly. Eight months later she saved another $ 5000. Find the amount in the account two years after her first saving.

5000*1.01^8 + 10000*1.01^16

To find the amount in the account two years after the first saving, we need to calculate the compounded interest for each period and add it to the principal amount.

First, let's calculate the interest for the first $5000 saved for eight months. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount (initial savings)
r = Annual interest rate (12% or 0.12)
n = Number of times the interest is compounded per year (monthly compounding, so n = 12)
t = Time in years (8 months = 8/12 = 2/3 years)

Plugging in the values:

A1 = 5000(1 + 0.12/12)^(12 * 2/3)
A1 ≈ 5000(1 + 0.01)^(8)
A1 ≈ 5000(1.01)^8
A1 ≈ 5000(1.082432)
A1 ≈ 5412.16

The amount after eight months is $5412.16.

Now, let's calculate the interest for the second $5000 saved for two years (24 months).

A2 = 5000(1 + 0.12/12)^(12 * 2)
A2 ≈ 5000(1 + 0.01)^(24)
A2 ≈ 5000(1.01)^24
A2 ≈ 5000(1.268242)
A2 ≈ 6341.21

The amount after two years for the second saving is $6341.21.

To find the total amount in the account two years after the first saving, we add the two savings:

Total amount = A1 + A2
Total amount ≈ 5412.16 + 6341.21
Total amount ≈ 11753.37

Therefore, the amount in the account two years after 's first saving is approximately $11,753.37.