Related Rates: Quiz
Problem 5
A savings account is set up so that a regular deposit of $150 is made every month. The account earns interest, and the interest varies according to the amount in the account: An account with balance B less than $100 earns no interest; otherwise, the interest rate is 2.7% plus .05% for each $1000 in the account, up to $10,000.
Find the rate of change of interest I with respect to time t.
Answers, problem 5
dB/dt = 150, where t is measured in months.
dI/dB = .05%/1000 = 0.0000005
Therefore dI/dt = (dI/dB)(dB/dt) = (0.0000005)(150) = 0.000075 or 0.0075% per month.