Question: The amount of money, A(t), in a savings account after t years of continuously compounding interest is given by the function A(t) = A (0) ert. suppose that the money in the account grew from $1000 to $ 8000 in 3 years, what would be the money in the account at the end of 4th year?
A ) $16000 B ) $15000 C ) $10000 D ) $12000
Steps to derive
1 The amount of money A(t), in the savings account grows with time t as A(t) = A (0) ert where A (0) is the initial amount in the account which is $ 1000.
2 Since after 3 years the amount in the account is $8000, A (3) = 8000.
3 A (0) e3r = 8000 [Substitute 3 for t in A(t).]
4 1000 e3r = 8000 [Substitute $1000 for A(0).]
5e3r = 8 [Simplify.]
6er = 2 [Solve for er.]
7 The amount at the end of the 4th year = A (4) =A(0)e4r. [Substitute 4 for t in A(t).]
8 = (1000)(24) [Substitute 2 for er and 1000 for A (0).]
