Question

What single payment today would replace a payment stream of $50,000 that will be paid today, again at the end of year 1, and again at the end of year 2, if money earns 4% compounded semi-annually?

Select one:

a. $94,384.98

b. $97,484.92

c. $85,865.39

d. $93,485.53

e. $98,058.44

Answer 1

The formula for compound interest, including principal sum, is:
A = P (1 + r/n) ^(nt)

^{Interest rate 4% Compounded semi annually}

^{Effective Annual Interest rate =} (1+ 4%/2) * (1+4%/2) = 1.0404 i.e 4.04%

Year	PVF	Installment	Present Value
1	0.961169	50000	48058.43906
2	0.923845	50000	46192.2713

Total of Present value = 48058 + 46192.2713

              = 94250.71036

So, option “a” is correct.