Mel\'s Money Market offers an investment account that guarantees an annual rate
ID: 1890275 • Letter: M
Question
Mel's Money Market offers an investment account that guarantees an annual rate ofretun of 4%, so that after t years an investment of Ao dollars will be worth a total amount, A, as given by A= Ao(1.04)^t dollars.
(a) Write a formula for A in the form A= Aoe^rt. Give both the exact value of r and an approximation of r correct to four decimal places.
(b) How long would ittake for a single deposit of Ao dollars to double in value? give your answer to the nearest tenth of a year ans show how you arrived at your conclusion
Ao means A substript of zero
Explanation / Answer
to write in the form ==> (1.04)^t = e^rt. ==> r = 0.03922071315328129626920089657112 = 3.922071315328129626920089657112% exact r (aproxx) = 3.9221 % (b) A= Ao(1.04)^t and given A = 2 Ao ==> (1.04)^t = 2 ==> t = 17.673 years Rounding of to nearest 10th of a yer = 20 years