A = 1000× (A/F, 2%, 4) = 1000× 0.2426 = 242.60 (ten thousand yuan)
Then use the formula F = A (F/A, I, N) to convert it to the end of the 20th century (that is, the end of the 5th year), that is, the sum of the principal and interest of this investment at the end of the 5th year.
F = a× (f/a, 2%, 20) = 242.60× 24.2974 = 5894.55 (ten thousand yuan)
Then use the formula of equal payment present value P = A (P/A, I, N) to convert to the beginning of the first year, which is the present value of this investment. P = a× (p/a, 2%, 20) = 242.60×16.3514 = 3966.85 (ten thousand yuan).
Scheme 2: Organize the original cash flow statement into quarterly interest period, and then use the one-time payment formula f = p (f/p, i, n) to convert the investment of 12, 16, and the end of 20th quarter into the end of 20th quarter (that is, the end of 5th year).
F= 1000× (financial ratio, 2%, 16)+ 1000× (financial ratio, 2%, 12)+ 1000× (financial ratio, 2%)
= 1000× 1.3728+ 1000× 1.2682+ 1000× 1. 17 17+ 1000.
Then, the one-off present value formula p = f (p/f, I, N) is used to convert the investment100000 at the end of the 4th, 8th, 12, 16 and 20th quarters to the beginning of the first quarter (that is, the beginning of the first year) respectively, so as to obtain the present value of this investment.
P= 1000×(P/F，2%，20)+ 1000×(P/F，2%， 1000)×(P/F，2%， 12)+ 1000×(P/F，2%，8)+ 1000×(P/F，2%，4)
= 1000 × 0.6730+ 1000 × 0.7284+ 1000 × 0.7885+ 1000 × 0.9238 = 3967.
Scheme 3: Calculate the annual real interest rate first, and then convert it to the end of the fifth year by formula F = A (F/A, I, N), which is the sum of the principal and interest of this investment at the end of the fifth year.
ieff =( 1+8%÷4)- 1 = 8.24%
F = a× (f/a, 8.24%, 5) =1000× [(1+8.24%)-1] ÷ 8.24% = 5894.74 (ten thousand yuan).
The present value of this investment is obtained by converting the sum of principal and interest at the end of the fifth year into the sum of principal and interest at the beginning of the first year with the present value formula of one-time payment P = F (P/F, I, N).
P = f× (p/f, 8.24%, 5) = 5894.74 ÷ (1+8.24%) 5 = 3967.58 (ten thousand yuan).