Jennifer borrowed $20,000 from her best friend, two years later, Jennifer repaid her $22,050. Calculate the effective annual interest rate.

Question

BlackTom AI · Accepted Answer

We start by restating the problem: Jennifer borrows 20,000 and repays 22,050 after 2 years. We need the effective annual interest rate.
Option A: 4.65%.
If the annual rate were 4.65%, the growth over 2 years would be (1+0.0465)^2 = 1.0937 approximately, meaning the amount would grow to about 20,000 × 1.0937 ≈ 21,874, which is far below the repaid 22,050. Therefore, 4.65% underestimates the rate.
Option B: 5.00%.
With an annual rate of 5%, the accumulation over 2 years is (1+0.05)^2 = 1.1025. Multiplying 20,000 by 1.1025 yields 22,050 exactly, matching the given repayment. This is consistent with the data, so 5.00% is a correct fit.
Option C: 10.25%.
An annual rate of 10.25% would compound to (1+0.1025)^2 ≈ 1.2155 over two years, producing about 24,310 on a 20,000 principal, which is far higher than 22,050. This option overstates the rate significantly.
Option D: 5.13%.
Using 5.13% gives (1+0.0513)^2 ≈ 1.1059, and 20,000 × 1.1059 ≈ 22,118, which is not equal to 22,050. Thus 5.13% is not the correct effective rate.
In summary, the only option that yields the exact two-year accumulation matching 22,050 is 5.00%, since (1+0.05)^2 = 1.1025 and 20,000 × 1.1025 = 22,050.

25400 Financial Literacy - Spring 2025 🔴 Practice Questions 1 Compound Interest

Jennifer borrowed $20,000 from her best friend, two years later, Jennifer repaid her $22,050. Calculate the effective annual interest rate.

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