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
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.
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