If $5200 is placed in an account which pays 7% per annum, compounding annually, then the balance in the account after n years is calculated by:

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The problem describes an initial principal of $5200 invested at an annual interest rate of 7% with annual compounding. To model the balance after n years, we use the compound interest formula: Final amount = Principal × (1 + rate)^{n}.

Option A: $364n. This expression represents simple arithmetic growth, not compounding, and uses a linear growth based on n. It ignores the exponential effect of compounding and the correct base multiplier 1.07. Therefore, it is incorrect.

Option B: $5200 × 7n. This option multiplies the principal by 7n, which would imply a linear growth scaled by n and uses 7 as a multiplier, not the 1.07 growth factor per year. It misapplies both the rate and the compounding concept, so it is incorrect.

Option C: $5200 × 0.7^n. This uses 0.7 as the annual growth factor, which would imply a huge decrease each year (since 0.7 < 1), corresponding to a negative scenario like depreciation, not interest accrual. It incorrectly uses 0.7 instead of 1.07, so it is incorrect.

Option D: $5200 × 1.07^n. This aligns with the standard compound interest formula, where each year the balance is multiplied by 1 + 0.07 = 1.07, and after n years the growth is exponential with exponent n. It correctly represents annual compounding at 7% on the initial principal, so it is correct.

In summary, the only option that faithfully applies the compound-interest model with annual compounding at 7% is the one using the principal multiplied by 1.07 raised to the power n. The other options misrepresent either linear growth, incorrect base, or misuse of the compounding concept.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

If $5200 is placed in an account which pays 7% per annum, compounding annually, then the balance in the account after n years is calculated by:

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