A bank pays interest at the rate r, compounded M times yearly. The effective interest rate re is the rate at which interest, if compounded annually, would have to be paid to produce the same yearly return. (a) Find re if r = 9% compounded monthly. (b) Show that re = (1 + r/M)M − 1 and that re = er − 1 if interest is compounded continuously. (c) Find re if r = 11% compounded continuously. (d) Find the rate r that, compounded weekly, would yield an effective rate of 20%.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
A bank pays interest at the rate r, compounded M times yearly. The effective interest rate re is the rate
at which interest, if compounded annually, would have to be paid to produce the same yearly return.
(a) Find re if r = 9% compounded monthly.
(b) Show that re = (1 + r/M)M − 1 and that re = er − 1 if interest is compounded continuously.
(c) Find re if r = 11% compounded continuously.
(d) Find the rate r that, compounded weekly, would yield an effective rate of 20%.
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