How to Solve Interest Theory — Time Value of Money — simple interest and simple discount accumulation, present value, and rate Questions on Exam FM

Exam FM Topic: Interest Theory — Time Value of Money — simple interest and simple discount accumulation, present value, and rate Verified Procedural Question
Sample Practice Problem ID: #7IZ5P
At the beginning of each year for \(10\) years, \(100\) is deposited into the municipal archive preservation program. Under simple annual interest, the value at the end of year \(10\) is \(1,220\). Using the simple rate implied by that value, calculate the account value at the same date if interest had instead compounded annually at that effective rate.
(A)1248.6351
(B)832.4234
(C)1220.0000
(D)1206.3979
(E)936.4763
📖 Worked Solution & Strategy
The deposits earn simple interest for \(1,2,\ldots,10\) years, so \(100[10+i(55)]=1,220\). This gives \(i=0.040000\). Under annual compounding, the deposits form an annuity-due and accumulate to \(100\ddot{s}_{10|0.040000}=1248.6351\). Thus the compound-interest value is \(1248.64\).
Therefore, the result is \(\frac{100 \left(0.000181818181818182 a + 0.818181818181818\right) \left(\left(0.000181818181818182 a + 0.818181818181818\right)^{10} - 1\right)}{0.000181818181818182 a - 0.181818181818182}\approx 1248.6351\), so the correct answer is option (A).

Final Answer: Option (A)

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