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
Accepted Solution
A:
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