You could borrow $2,000 today from Bank A and repay the loan,with interest,by paying Bank A $2,125 one year from today.Or,you could borrow X dollars today from Bank B and repay the loan,with interest,by paying Bank B $2,200 two years from today.In order for the same interest rate to apply to the two loans,X =
A)$1,853.55.
B)$1,898.70.
C)$1,948.79.
D)$2,012.22.

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we can set up two equations:

Bank A: $2,000(1+r)^1 = $2,125
Bank B: X(1+r)^2 = $2,200

Solving for r in Bank A's equation, we get r = 0.0625 or 6.25%
Substituting r into Bank B's equation, we get X = $1,948.79 to have the same interest rate.
Therefore, choosing Bank B with loan amount $1,948.79 would be the better choice as it offers a higher loan amount and the same interest rate as Bank A's offer.

You Could Borrow $2,000 Today from Bank a and Repay