Question

The function r(t) = 0.69607 + 0.60781 ln t gives the annual interest rate r, as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested) in months.

(a) What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 10 months? (Round your answer to one decimal place.)

(b) What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 3.0%? (Round your answer to the nearest whole number.)

Answer 1

Given, the annual interest rate as a function of time is

r(t) = 0.69607 + 0.60781 ln t

for 10 months,

r(10) =  0.69607 + 0.60781 ln(10)

=  0.69607 + 0.60781 X 2.30258509299

= 0.69607+1.39953424537

= 2.09560424537

2.1% after rounding off to one decimal place.

b)

Interest rate atleast of 3% so,

3 =  0.69607 + 0.60781 ln t

Implies, 3.79054 = ln t

ln t =  3.79054

Applying exponential on both sides, we get

t = e^3.79054​

t = 44.2803051859

Mininum of 45 Complete months is necessary to achieve 3% interest rate.