Three siblings, Ronnie, Connie, and Bonnie, want to borrow $150,000 each so that

Question

Three siblings, Ronnie, Connie, and Bonnie, want to borrow $150,000 each so that they can purchase a vacation home in Trinidad. All three agree to repay their loans in full in one year using the inheritance they plan to receive from a wealthy relative. Ronnie borrows his money at six percent, compounded monthly. Connie borrows her money at six percent, compounded annually. Bonnie agrees to a loan with six percent simple interest. Which of the following statement is true?

A. Ronnie, Connie, and Bonnie will each owe the same amount one year from now.

B. Ronnie will have to repay less money than either Connie or Bonnie.

C. Connie will have to repay the same amount as Ronnie, but less than Bonnie.

D. Bonnie will owe less money than either Connie or Bonnie.

E. Connie will owe the same amount as Bonnie, but less than Ronnie.

Explanation / Answer

Repayment = PV x (1 + r/n)^n - 1

Ronnie's repayment = 150,000 x (1 + 6%/12)^12 - 1 = $159,252

Connie's repayment = 150,000 x (1 + 6%/1)^1 - 1 = $159,000

Bonnie's repayment = 150,000 x (1 + 6%) = $159,000

Hence, E is correct.

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