Mr. mady opens a savings account with principal p dollars that pays 4.11% interest compounded quarterly. express his ending balance after one year algebraically.

At the end of one year, and at the current rate of increase, Mr. Mady's account would be P x 1.010275⁴

Because the amount is compounded quarterly, the period and the interest rate need to be changed to quarterly figures:

Period = 1 year x 4 quarters = 4 quarters

Interest = 4.11% / 4 quarters = 1.0275% .

The amount after a year is:

= Amount x ( 1 + rate) ^ number of periods

= P x ( 1 + 1.0275%)⁴

= P x 1.010275⁴

In conclusion, the balance after a year is P x 1.010275⁴.

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Answer

Find out the  ending balance after one year algebraically.

To proof

Formula of compound interest quarterly

where

P = principle

R = rate of interest

n = time period in the years

As given

Mr. Mady opens a savings account with principal P dollars that pays 4.11%

interest compounded quarterly

Time = 1 year

put in the equation

we get

solving the above

Solving

= 1.0417P ( approx )

ending balance after one year is $1.0417P ( approx )

Hence proved

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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