For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:
A
555.
B
563.
C
576.
A is correct.
The effective annual rate (EAR) is calculated as follows:
EAR = (1 + Periodic interest rate)m – 1 EAR = (1 + 0.03/365)365 – 1 EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%.
Solving for N on a financial calculator results in (where FV is future value and PV is present value):
(1 + 0,030453）^N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, which multiplied by 12 to convert to months results in 554.5, or ≈ 555 months.
