Accounting

Please help me with the calculations.

 

 

 

 

 

 

 

 

 

Accounting assignment

 

 

 

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Accounting assignment

If you presently have $20,000 invested at a rate of 12% per annum approximately how many years will it take for the investment to triple?

Assume FV is the future value, P is cash flow per period, r denotes interest rate and n the number of years

Triple investment = 20,000* 3 = 60,000

The future value can be compounded using the formulae, FV= P (1+r)ⁿ

60,000 = 20,000 (1+0.12)^t

                                             60,000/20,000 = 20,000/20,000 (1+0.12)^t

                                              3 = (1.12) t

n * log 1.12 = log 20,000

n = log 3 /log 1.12

n = 9.694 years or 9 years and 9 months

n= 10 years

 

Assume you purchase a car for $1,500,000 on terms of 20% down payment, with the balance to be paid off quarterly over 3 years at a rate of 8% on the paid balance

1. What are the equal quarterly payments?

Down payment = 20% * 1,500,000 = $300,000

Balance            = 1,500,000-300,000

=$ 1,200,000

Equal quarterly instalments (EQI) = P* r (1+ r)ⁿ / ((1+r)ⁿ -1)

EQI = 1,200,000* 0.02 (1.02)¹² / 1.02¹² -1

EQI = 30437.803/ 0.26824

EQI = $ 113,472.275

 

1. Prepare the amortization schedule for the quarterly payments

 

 

PmtNo.	Opening Balance	Total Monthly Repayment	Principal Due	Interest Due	Closing Balance
1.00	1,200,000.00	113,472.28	107,472.28	6,000.00	1,092,527.73
2.00	1,092,527.73	113,472.28	108,009.64	5,462.64	984,518.09
3.00	984,518.09	113,472.28	108,549.68	4,922.59	875,968.40
4.00	875,968.40	113,472.28	109,092.43	4,379.84	766,875.97
5.00	766,875.97	113,472.28	109,637.90	3,834.38	657,238.08
6.00	657,238.08	113,472.28	110,186.08	3,286.19	547,051.99
7.00	547,051.99	113,472.28	110,737.02	2,735.26	436,314.98
8.00	436,314.98	113,472.28	111,290.70	2,181.57	325,024.28
9.00	325,024.28	113,472.28	111,847.15	1,625.12	213,177.12
10.00	213,177.12	113,472.28	112,968.39	1,065.89	100,770.73
11.00	100,770.73	100,770.73	100,266.88	503.85	–
12.00	–	–	–	–	–

 

A young man wishes to accumulate $850,000 at the end of five years so that he may make a down payment on a house which will cost $12,250,000

1. what should his equal end of year deposit be to accumulate $850,000 at 4% rate of interest

 

Future value = P * ((1+r)ⁿ – 1)/r))

$850,000 = P ((1.04)⁵ -1)/0.04)

                   $850,000 = P (5.4163)

                                P = 850,000/5.4163

                                P = 156,933.

                               End of year deposit =$156,933

This is a problem related to future value of an ordinary annuity (Chan & Tse, 2017).

1. If the young man receives the remaining portion of the cost of the house from a financial institution at a rate of 6% to be repaid monthly over 15 years, calculate the monthly payment for this loan

 

Remaining portion = $12,250,000-$850,000

= $11,400,000

 

Monthly interest rate = 6%/12

= 0.5%

 

 

Monthly instalments (MI) = P* r (1+ r)ⁿ / ((1+r)ⁿ -1)

MI = 11, 400,000* 0.005(1.005)¹⁸⁰/ 1.005¹⁸⁰ -1

MI   =$ 96,199.7

If you wish to save $1,200,000 in three years, how much would you need to deposit at the start of each quarter to achieve this goal assuming an interest rate of 6% compounded quarterly.

Let P be the amount I wish to save and deposit be D

P = D *((1+r)ⁿ – 1)/r)*(1+r)

$1,200,000 = D ((1.015)¹² -1)/0.015)*(1+0.015)

$1,200,000 = D (13.04121)*1.015

                                D= 1,200,000/13.2368

                                D = $ 90,656.15

 

What is the present value of an annual annuity payment of $12,000 made for 10 years with a discount rate of 5% and with a first payment starting today.

This is an example of an annuity due problem ( Ortiz-Betancourt et al, 2017).

Present value of annuity due = D ((1-(1+r) ^–n )/r))* (1+r)

= 12,000* ((1-(1.05^-10)/0.05))*(1.05)

=$97,293.86

 

 

 

 

 

 

 

 

You expect to deposit the following cash flows at the end of years 1 through 5, $17,000, $14,000,$19,000,$25,000 and $20,000 respectively. What is the future account value at the end of year 6 if you can earn 8% compounded annually?

 

 

 

 

 

0             1                  2             3                 4               5

 

17,000*(1.08)⁰  = 17,000.00

14,000*(1.08)¹ = 15,120.00

19,000*(1.08)² = 22,161.60

25,000*(1.08)³ = 31,492.80

20,000*(1.08)⁴  = 27,209.79

FV =17,000+15120+22,161.6+31,492.8+27,209.79

=112,984.19 in 5 years

By the end of the 6^th year the value will be 112,984.19*(1.08)

= $ 122,022.83

 

     National commercial bank will loan you $132,250 for three years to buy a computer. The loan must be repaid in 36 equal monthly payments. The annual interest rate on the loan is 12 percent of the unpaid balance. How large are the monthly payments.

 

Equal monthly instalments (EMI) = P* r (1+ r)ⁿ / ((1+r)ⁿ -1)

EMI = 132, 250* 0.01 (1.01)³⁶ / 1.01³⁶ -1

EMI = 132,250*0.033214

EMI = $ 4,392.59

 

 

 

References

 

Chan, W. S., & Tse, Y. K. (2017). Financial mathematics for actuaries. World Scientific Publishing Company.

Ortiz-Betancourt, I., García-Santillán, A., Solano-García, C., & Martínez-Utrera, V. (2017). AN Investment Fund as an Element Of Financial Education In Personal Finance.