Please explaine it step by step Caveman Manufacturing took out a loan for specia
ID: 2469389 • Letter: P
Question
Please explaine it step by step
Caveman Manufacturing took out a loan for specialized manufacturing equipment requiring six large loan payments in the future. Caveman will make the first payment of $25086 at the end of year 20 and each subsequent payment will increase by $8600 over the previous year. Caveman would like to save for these large payments by making 19 equal deposits at the end of each year. What amount must Caveman deposit each year in order to make the future loan payments? Assume an interest rate of 2.5% compounded annually.Explanation / Answer
First repayment at the end of year 20 = $25,086
Each subsequent payment shall increase by $8,600.
Hence, the six repayments shall be as below:
Year
Payment
20
$25,086.00
21
$33,686.00
22
$42,286.00
23
$50,886.00
24
$59,486.00
25
$68,086.00
The present value of these payment at the end of year 19 shall be as below:
Year
Payment
Discounting period
Present value factor @ 2.5%
Present value
20
$25,086.00
1
0.9756
$24,473.90
21
$33,686.00
2
0.9518
$32,062.33
22
$42,286.00
3
0.9286
$39,266.78
23
$50,886.00
4
0.906
$46,102.72
24
$59,486.00
5
0.8839
$52,579.68
25
$68,086.00
6
0.8623
$58,710.56
$2,53,195.97
Thus, Caveman need to have $253,195.97 in the deposit account at the end of year 19 to pay the future six payments.
Future value of equal 19 annual deposits = $253,195.97
Future value of annuity = Annuity *{(1+r)n – 1}/r
$253,195.97 = Annuity * (1.02519 – 1)/0.025
$253,195.97 = Annuity * 23.9460
Annuity = $253,195.97/23.9460 = $10,573.62
Hence Caveman need to deposit $10,573.62 annually for next 19 years.
Year
Payment
20
$25,086.00
21
$33,686.00
22
$42,286.00
23
$50,886.00
24
$59,486.00
25
$68,086.00