Question

At the beginning of year 1, Bode invests $250 at an annual simple interest rate of 3%. He makes no deposits to or withdrawals from the account.Which explicit formula can be used to find the account’s balance at the beginning of year 14? What is the balance?
A.A(n) = (250)(n – 1)(0.03); $97.50 B.A(n) = 250 + (n)(0.03 • 250); $355.00 C.A(n) = 250 + (n – 1)(0.03); $250.39 D.A(n) = 250 + (n – 1)(0.03 • 250); $347.50

Answer 1

Answer:

the correct answer is D

Step-by-step explanation:

i just did it and it was right

Answer 2

The initial investment = $250
annual simple interest rate of 3% = 0.03

Let the number of years = n
the annual increase = 0.03 * 250
At the beginning of year 1 ⇒ n = 1 ⇒⇒⇒ A(1) = 250 + 0 * 250 * 0.03 = 250

At the beginning of year 2 ⇒ n = 2 ⇒⇒⇒ A(2) = 250 + 1 * 250 * 0.03
At the beginning of year 3 ⇒ n = 3 ⇒⇒⇒ A(2) = 250 + 2 * 250 * 0.03
and so on .......
∴ The formula that can be used to find the account’s balance at the beginning of year n is:

A(n) = 250 + (n-1)(0.03 • 250)
At the beginning of year 14 ⇒ n = 14 ⇒ substitute with n at A(n)
∴ A(14) = 250 + (14-1)(0.03*250) = 347.5

So, the correct option is D.A(n) = 250 + (n – 1)(0.03 • 250); $347.50