Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end ofeach year for 20 years at the given interest rate, compounded annually).
-$\$ 12,600$ at $8 \%$
A) $\$ 123,708.66$
B) $\$ 123,671.52$
C) $\$ 121,005.36$
D) $\$ 126,211.68$

Question

Quizplus · Accepted Answer

The future value of the annuity is:FV = PMT * [(1 + r)^n - 1] / r= 12600 * [(1 + 0.08)^20 - 1] / 0.08= 12600 * [2.158925 - 1] / 0.08= 12600 * 1.158925 / 0.08= 12600 * 14.4865625= 182,324.41The present value of the lump sum is:PV = FV / (1 + r)^n= 182,324.41 / (1 + 0.08)^20= 182,324.41 / 6.386143= 28,553.48Therefore, the lump sum that will yield the same total amount as the yearly payment is $28,553.48.

Find the Lump Sum Deposited Today That Will Yield the Same