__BANK FINANCIAL MANAGEMENT NUMERICALS : 4__

ABM/BFM NUMERICALS

ABM/BFM NUMERICALS

1. You are receiving Rs. 10000 every year for the next 5 years (at the beginning of the period) and you invest each payment @ 5%. How much you would have at the end of the 5-year period?

Explanation :

Here, P = 10000

R = 5% p.a.

T = 5 yrs If invested at the beginning, FV = P / R * [(1+R)^T - 1] * (1+R) FV = 55256 × 1.05

= 58019

2. If you wish an annuity to grow to Rs. 17000 over 5 years so that you can replace your car, what monthly deposit would be required if you could invest @ 12% compounded monthly?

Explanation :

Here, FV = 17000

T = 5 years = 60 months

R = 12% yearly = 0.01% monthly

P =? FV = P / R * [(1+R)^T - 1] 17000 = P × (1.01^60 – 1) ÷ 0.01

17000 = P × 81.6697 So,

P = 17000 / 81.6697

= 208

3. What amount you would need to invest in the annuity if you want to get paid Rs. 20,000 a year for 20 years when the roi is 5%?

Explanation :

Here, 20000 is to be get paid each year, so the formula is derived from EMI formula: PV = P / R * [(1+R)^T - 1]/(1+R)^T PV = 20000 × (1.0520 – 1) ÷ (0.05 × 1.0520)

= 249244

4. Find the present value of quarterly payment of Rs. 250 for 5 years @ 12% compounded quarterly.

Explanation :

Here, P = Rs. 250

T = 5 years = 5 × 4 = 20 quarters

R = 12% = 12% ÷ 4 = 0.03% quarterly PV = P / R * [(1+R)^T - 1]/(1+R)^T PV = 250 × (1.0320 – 1) ÷ (0.03 × 1.0320)

= 3719

5. A sum of Rs. 25, 000 is borrowed over 8 years. What will be the monthly repayments @ 18% compounded monthly?

Explanation :

Here, PV = Rs. 25000

T = 8 years = 8 × 12 = 96 months

R = 18% = 18% ÷ 12 = 0.015% monthly PV = P / R * [(1+R)^T - 1]/(1+R)^T 25000 = P × (1.01596 – 1) ÷ (0.015 × 1.01596)

25000 = P × 50.7017

P = 25000 / 50.7017

= 493

6. How much money will a student owe at graduation if she borrows Rs. 3000 per year @ 5% interest during each of her four years of school?

Explanation :

Here, P = Rs. 300

T = 4 years

R = 5% FV = P / R * [(1+R)^T - 1] FV = 3000 × (1.054 – 1) ÷ 0.05

= 12930

7. A construction company plans to purchase a new earth mover for Rs. 350000 in 5 years. Determine the annual savings required to purchase the earthmover if the return on investment is 12%.

Explanation :

Here, FV = Rs. 350000

T = 5 years

R = 12% FV = P / R * [(1+R)^T - 1] 350000 = P × (1.125 – 1) ÷ 0.12

350000 = P × 6.3528

P = 350000 / 6.3528

= 55094

8. A man borrowed a certain sum of money & paid it back in 2 years in two equal installments. If the roi (compound) was 4% p.a. and if he paid back Rs. 676 annually, what sum did he borrow?

Explanation : Here, PV =?

P = Rs. 676

T = 2 years

R = 4% = 0.04 PV = P / R * [(1+R)^T - 1]/(1+R)^T PV = 676 × (1.042 – 1) ÷ (0.04 × 1.042)

= 1275

9. A sum of Rs. 32800 is borrowed to be paid back in 2 years by two equal annual installments allowing 5% compound interest. Find the annual payment.

Explanation : Here, PV =?

P = Rs. 32800

T = 2 years

R = 5% = 0.05 PV = P / R * [(1+R)^T - 1]/(1+R)^T 32800 = P × (1.052 – 1) ÷ (0.05 × 1.052)

P = 32800 ÷ 1.8594

P = 17640

10. A loan of Rs. 4641 is to be paid back by 4 equal annual installments. The interest is compounded annually @ 10%. Find the value of each installment.

Explanation : Here, PV =?

P = Rs. 4641

T = 4 years

R = 10% = 0.10% EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 4641 × 0.1 × 1.14 ÷ (1.14 – 1)

= 1464

11. A loan of Rs. 1 lac is paid back in 5 equal annual installments. The roi charged is 20% annually. Find the amount of each loan?

Explanation :

Here, FV = Rs. 100000

T = 5 years

R = 20% p.a. = 0.2% EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 100000 × 0.2 × 1.25 ÷ (1.25– 1)

= 33438

12. A person wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2 years @ 10% interest. He wants to pay it in monthly installments for 5 years. Calculate the amount of monthly payment? Explanation : Here, PV of 20000 for 2 years @ 10% = 20000 ÷ 1.0083324 = 16388.07

So, total amount = 25000 + 16388.07 = 41388.07

Now, T = 5 × 12 = 60 months and R = 10% p.a. = 10/1200 = 0.00833 EMI = P * R * [(1+R)^T/(1+R)^T-1)] EMI = 41528.93 × 0.00833 × 1.0083360 ÷ (1.0083360 – 1)

= 879

13. You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current discount rate for such a stream of cash flow is 10%, find the present value of cash flow.

Explanation :

Here, P = 204000

R = 10

T = 20 PV = P / R * [(1+R)^T - 1]/(1+R)^T PV = 1736770

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