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

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

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