Raymond made a deposit of 10000 into his savings account. Four years later he made a second deposit of 1000. How much is in his account 6 years after the first deposit, if the interest rate is 15% compounded annually?
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Let's start with the first deposit of 10000. We don't know the frequency of compounding, so let's assume it is compounded annually (n = 1).
After four years, the amount in the account is:
A = 10000(1 + 0.15/1)^(1*4)
A = 16435.03
Now, let's add the second deposit of 1000, and assume it is also compounded annually:
A = (10000 + 1000)(1 + 0.15/1)^(1*2)
A = 12822.50
Finally, we want to know how much is in the account 6 years after the first deposit. We can use the final amount from the previous calculation as the principal for a new calculation:
A = 12822.50(1 + 0.15/1)^(1*4)
A = 22068.24
Therefore, the amount in Raymond's account 6 years after the first deposit is $22,068.24.