Question

You purchase an annuity investment that pays you a lump sum amount of $289,284 at the end of the term. You must make $20,000 quarterly payments until the end of the term. If you earn an interest rate of 2%, how many of these quarterly payments must you make? (Round to the nearest whole number)

Answer 1

SOLUTION:-
0.5% [2% / 4; Annual rate is converted into quarterly rate] $20,000 Quarterly Interest Rate, RATE Quarterly payments, PMT Initial lumpsum payment, PV Maturity amount at the end, FV Quarterly payment type, TYPE #of Quarterly payments required $289,284 0 = 0 If deposits made at the end of each period; 1 if deposits made at the beginning of each period 14 [Ref: NOTE] NOTE: #of Quarterly payments required is calculated using EXCEL FUNCTION NPER(rate,pmt,pv.fv,type) where rate=0.5%; pmt = 20000; pv = 0; fv = -289284; type=0; Here, value for pmt is positive as it denotes cash outflow; fv is negative as it denotes cash inflow; type=0 as deposits made at the end of each quarter only. D F G H I 1 Quarterly Interest Rate, RATE =2%/4 [2%/4; Annual rate is converted into quarterly rate] 2 Quarterly payments, PMT $20,000 3 Initial lumpsum payment, PV 4 Maturity amount at the end, FV $289,284 5 Quarterly payment type, TYPE 0 = 0 if deposits made at the end of each period; 1 if deposits made at the beginning of each period 6 # of Quarterly payments require ENPER(C1,C2,C3,-C4,C5) (Ref: NOTE]