A bank offers two different retirement savings plans to its customers.

Question

For the first offer, the bank will match every dollar deposited up to $450, at which point all funds in the account will collect 3% interest annually. The second offer has no price matching, but instead pays an interest rate of 7%. At what principal value are the two accounts an identical investment after one year?

A) $866.35

B) $2257.83

C) $4562.43

D) $11587.50

Answer 1

Assume that the amount invested, x, is equal to or greater than $450

0.03(450 + x) = 0.07x

13.5 + 0.03x = 0.07x

13.5 = 0.04x

337.5 = x

Contradiction. The investment cannot be equal to or greater than $450.

Answer 2

The answer is D. In the first case, assuming that your investment P is > $450, then the net investment is P + $450 and the account balance after 1 year becomes (P + 450)(1.03). In the second case, the balance after 1 year is P*(1.07). Setting these balances equal to each other, 1.03 P + 463.50 = 1.07 P, P = 463.50/(0.04) = $11,587.50. The assumption that P > $450 is validated!