Question

4. Consider an annuity paying $150 every month at 18% compounded monthly. How many payments will be necessary and what would be the ballo payment, and fractional payment (as in Example 3.6) to amount to exactly $15,000?

Answer 1

1)
Pv	0
PMT	$150
Rate	1.63%
Future value	15000
Number of periods	59.80
2)
Amount accumulated at the end of 59th period
Pv	0
PMT	$150
Rate	1.63%
Nper	59.00
Future Value	$14,687.24
Drop Payment (15000 - 14,687.24)	$312.76
Fraction Payment = $150 + $312.76	$462.76
Balloon Payment
PV	$312.76
PMT	$0
Rate	1.63%
Nper	0.80
Future value (balloon payment)	$316.85

A 1 1) 2 Pv 3 PMT 4 Rate 5 Future value 6 Number of periods 0 150 =(EFFECT(18%,12}}/12 15000 =NPER(B4,B3,B2,-35) 9 Amount accumulated at the end of 59th period 10 Pv PMT Rate Nper Future Value 0 150 =(EFFECT(18%,12}}/12 59 =FV(B12,113,-B11,810) Drop Payment (15000 - 14,687.24) Fraction Payment = $150 + $312.76 =B5-B14 =B16+B11 19 Balloon Payment 20 PV =B16 21 PMT 22 Rate 23 Nper Future value (balloon payment) =B12 =B6-B13 =FV(B22,B23,-B21,-B20)