Answer:
option (A) $69,035
Explanation:
Data provided in the question:
Amount received at the time of joining = $39,000
Amount received each year = $10,000
Duration, n = 5 years
Time value of money, r = 9% = 0.09
Now,
The single-sum equivalent
= $39,000 + Present value of a $10,000 deferred annuity
also,
Present value of the deferred annuity = $10,000 ×
on substituting the respective values, we get
Present value of the deferred annuity = $10,000 ×
or
Present value of the deferred annuity = $10,000 × 4.23972
= $42,397
Equivalent amount at the time of joining of the differed annuity i.e n = 4 years before
= $42,397 × [ 1 ÷ (1 + r )ⁿ]
= $42,397 × [ 1 ÷ (1 + 0.09 )⁴]
= $42,397 × 0.70843
= $30,035
Hence,
The single-sum equivalent = $39,000 + $30,035
= $69,035
Hence,
The answer is option (A) $69,035