Question

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

Answer 1

Formula for amount after 1 year is,

Where P is principal and R is rate

Let us suppose that a person invested x dollars in first offer,

So for the first 450 dollars of x the amount becomes 900 dollars

for the rest (x - 450) amount an interest of 3 dollars is calculated per year

Hence, A =(x - 450)(1+0.03) = 1.03x - 463.5

So total amount is = 900 + 1.03x - 463.5

This should be equal to the amount in the second offer, A =x(1+ 0.07) = 1.07x

1.07x = 900 + 1.03x - 463.5

0.04x = 436.5

x = 10912.5