An annuity has end of quarter payments for 15 years and the payment at the end o

ID: 2725685 • Letter: A

Question

An annuity has end of quarter payments for 15 years and the payment at the end of the j-th quarter (j=1,2,....,60) is $100j. The payments are made directly into a savings account with a nominal interest rate of 6% payable monthly and they are left in the account. find the effective interest rate for a quarter and use it to compute the balance in the savings account immediately after the last payment.
the correct answer is 1.50751% for the effective quarterly interest and $251,477.70 for the accumulated value An annuity has end of quarter payments for 15 years and the payment at the end of the j-th quarter (j=1,2,....,60) is $100j. The payments are made directly into a savings account with a nominal interest rate of 6% payable monthly and they are left in the account. find the effective interest rate for a quarter and use it to compute the balance in the savings account immediately after the last payment.
the correct answer is 1.50751% for the effective quarterly interest and $251,477.70 for the accumulated value
the correct answer is 1.50751% for the effective quarterly interest and $251,477.70 for the accumulated value

Explanation / Answer

Quarters (j)

Payment

No. of quarters left

FV factor @1.50751%

$ 100.00

2.417643715

$ 241.76

$ 200.00

2.381738765

$ 476.35

$ 300.00

2.346367047

$ 703.91

$ 400.00

2.311520642

$ 924.61

$ 500.00

2.277191749

$ 1,138.60

$ 600.00

2.243372681

$ 1,346.02

$ 700.00

2.210055868

$ 1,547.04

$ 800.00

2.17723385

$ 1,741.79

$ 900.00

2.144899279

$ 1,930.41

$ 1,000.00

2.113044916

$ 2,113.04

$ 1,100.00

2.081663628

$ 2,289.83

$ 1,200.00

2.050748391

$ 2,460.90

$ 1,300.00

2.020292283

$ 2,626.38

$ 1,400.00

1.990288485

$ 2,786.40

$ 1,500.00

1.96073028

$ 2,941.10

$ 1,600.00

1.93161105

$ 3,090.58

$ 1,700.00

1.902924277

$ 3,234.97

$ 1,800.00

1.874663536

$ 3,374.39

$ 1,900.00

1.846822502

$ 3,508.96

$ 2,000.00

1.819394942

$ 3,638.79

$ 2,100.00

1.792374714

$ 3,763.99

$ 2,200.00

1.765755769

$ 3,884.66

$ 2,300.00

1.739532148

$ 4,000.92

$ 2,400.00

1.713697979

$ 4,112.88

$ 2,500.00

1.68824748

$ 4,220.62

$ 2,600.00

1.663174951

$ 4,324.25

$ 2,700.00

1.63847478

$ 4,423.88

$ 2,800.00

1.614141436

$ 4,519.60

$ 2,900.00

1.590169473

$ 4,611.49

$ 3,000.00

1.566553522

$ 4,699.66

$ 3,100.00

1.543288296

$ 4,784.19

$ 3,200.00

1.520368588

$ 4,865.18

$ 3,300.00

1.497789265

$ 4,942.70

$ 3,400.00

1.475545272

$ 5,016.85

$ 3,500.00

1.45363163

$ 5,087.71

$ 3,600.00

1.432043432

$ 5,155.36

$ 3,700.00

1.410775845

$ 5,219.87

$ 3,800.00

1.389824108

$ 5,281.33

$ 3,900.00

1.369183529

$ 5,339.82

$ 4,000.00

1.348849488

$ 5,395.40

$ 4,100.00

1.328817432

$ 5,448.15

$ 4,200.00

1.309082877

$ 5,498.15

$ 4,300.00

1.289641404

$ 5,545.46

$ 4,400.00

1.27048866

$ 5,590.15

$ 4,500.00

1.251620358

$ 5,632.29

$ 4,600.00

1.233032274

$ 5,671.95

$ 4,700.00

1.214720244

$ 5,709.19

$ 4,800.00

1.196680171

$ 5,744.06

$ 4,900.00

1.178908015

$ 5,776.65

$ 5,000.00

1.161399797

$ 5,807.00

$ 5,100.00

1.144151597

$ 5,835.17

$ 5,200.00

1.127159554

$ 5,861.23

$ 5,300.00

1.110419864

$ 5,885.23

$ 5,400.00

1.093928778

$ 5,907.22

$ 5,500.00

1.077682605

$ 5,927.25

$ 5,600.00

1.061677707

$ 5,945.40

$ 5,700.00

1.045910502

$ 5,961.69

$ 5,800.00

1.030377459

$ 5,976.19

$ 5,900.00

1.0150751

$ 5,988.94

$ 6,000.00

$ 251,477.56

The above table shows the calculation.

FV factor = ( 1+ quarterly rate)^(No. of quarters left)

Adding all the FVs, we will get $251477.56