We are given 10 different problems related to finance. They include calculations involving simple and compound interest, annuities, and loan amortization. We need to solve each of these problems.

1. Problem Description

We are given 10 different problems related to finance. They include calculations involving simple and compound interest, annuities, and loan amortization. We need to solve each of these problems.

2. Solution Steps

Problem 1: Simple Interest

Principal $P = 5000$, Rate $r = 6\% = 0.06$, Time $t = 3$ years.

Simple Interest $I = Prt$

Total Amount $A = P + I = P + Prt = P(1+rt)$

$I = 5000 \times 0.06 \times 3 = 900$

$A = 5000 + 900 = 5900$

Problem 2: Simple Interest

Principal $P = 12000$, Rate $r = 8\% = 0.08$, Time $t = 5$ years.

Simple Interest $I = Prt$

Total Amount $A = P + I = P + Prt = P(1+rt)$

$I = 12000 \times 0.08 \times 5 = 4800$

$A = 12000 + 4800 = 16800$

Problem 3: Compound Interest

Principal $P = 3000$, Rate $r = 5\% = 0.05$, Time $t = 4$ years, compounded annually.

$A = P(1+r)^t$

$A = 3000(1+0.05)^4 = 3000(1.05)^4 = 3000 \times 1.21550625 \approx 3646.52$

Problem 4: Compound Interest

Principal $P = 7500$, Rate $r = 4\% = 0.04$, Time $t = 6$ years, compounded semi-annually.

$r_{semi} = \frac{0.04}{2} = 0.02$, $n = 6 \times 2 = 12$

$A = P(1+r_{semi})^n$

$A = 7500(1+0.02)^{12} = 7500(1.02)^{12} = 7500 \times 1.26824179 \approx 9511.81$

Problem 5: Compound Interest

Principal $P = 100000$, Rate $r = 10\% = 0.10$, Time $t = 5$ years.

(i) Compounded Monthly

$r_{monthly} = \frac{0.10}{12} = 0.0083333...$, $n = 5 \times 12 = 60$

$A = P(1+r_{monthly})^n$

$A = 100000(1+0.0083333)^{60} = 100000(1.0083333)^{60} = 100000 \times 1.645308949 \approx 164530.89$

$I = A - P = 164530.89 - 100000 = 64530.89$

(ii) Compounded Quarterly

$r_{quarterly} = \frac{0.10}{4} = 0.025$, $n = 5 \times 4 = 20$

$A = P(1+r_{quarterly})^n$

$A = 100000(1+0.025)^{20} = 100000(1.025)^{20} = 100000 \times 1.63861644 \approx 163861.64$

$I = A - P = 163861.64 - 100000 = 63861.64$

Problem 6: Future Value of an Ordinary Annuity

Payment $PMT = 200$, Rate $r = 6\% = 0.06$, Time $t = 5$ years, compounded monthly.

$r_{monthly} = \frac{0.06}{12} = 0.005$, $n = 5 \times 12 = 60$

$FV = PMT \times \frac{(1+r_{monthly})^n - 1}{r_{monthly}}$

$FV = 200 \times \frac{(1+0.005)^{60} - 1}{0.005} = 200 \times \frac{(1.005)^{60} - 1}{0.005} = 200 \times \frac{1.34885015 - 1}{0.005} = 200 \times \frac{0.34885015}{0.005} = 200 \times 69.77003 \approx 13954.01$

Problem 7: Future Value of an Ordinary Annuity

Payment $PMT = 250000$, Rate $r = 10\% = 0.10$, Time $t = 5$ years, compounded annually.

$FV = PMT \times \frac{(1+r)^n - 1}{r}$

$FV = 250000 \times \frac{(1+0.10)^5 - 1}{0.10} = 250000 \times \frac{(1.1)^5 - 1}{0.10} = 250000 \times \frac{1.61051 - 1}{0.10} = 250000 \times \frac{0.61051}{0.10} = 250000 \times 6.1051 = 1526275$

Problem 8:

Initial Investment =

1

0

0

0

0. Annual withdrawal =

1

5

0

0. Interest rate = 4%. Number of years =

7. Let $A_n$ be the amount after $n$ years.

$A_0 = 10000$

$A_1 = A_0 (1+0.04) - 1500 = 10000(1.04) - 1500 = 10400 - 1500 = 8900$

$A_2 = A_1 (1.04) - 1500 = 8900(1.04) - 1500 = 9256 - 1500 = 7756$

$A_3 = A_2 (1.04) - 1500 = 7756(1.04) - 1500 = 8066.24 - 1500 = 6566.24$

$A_4 = A_3 (1.04) - 1500 = 6566.24(1.04) - 1500 = 6828.8896 - 1500 = 5328.8896$

$A_5 = A_4 (1.04) - 1500 = 5328.8896(1.04) - 1500 = 5542.045184 - 1500 = 4042.045184$

$A_6 = A_5 (1.04) - 1500 = 4042.045184(1.04) - 1500 = 4203.72699136 - 1500 = 2703.72699136$

$A_7 = A_6 (1.04) - 1500 = 2703.72699136(1.04) - 1500 = 2811.8760710144 - 1500 = 1311.8760710144$

$\approx 1311.88$

Problem 9: Present Value of an Annuity Due

Cash Price = 40000

Installment Plan: 8 equal yearly installments at the beginning of each year. Rate = 12%

Let $PMT$ be the amount of each installment.

$PV = PMT \times \frac{1 - (1+r)^{-n}}{r} \times (1+r)$

$40000 = PMT \times \frac{1 - (1+0.12)^{-8}}{0.12} \times (1+0.12)$

$40000 = PMT \times \frac{1 - (1.12)^{-8}}{0.12} \times 1.12$

$40000 = PMT \times \frac{1 - 0.403875}{0.12} \times 1.12$

$40000 = PMT \times \frac{0.596125}{0.12} \times 1.12$

$40000 = PMT \times 4.967708333 \times 1.12$

$40000 = PMT \times 5.563833333$

$PMT = \frac{40000}{5.563833333} \approx 7188.29$

Problem 10: Amortization Schedule (Not able to prepare in text-only format)

Loan Amount = 42000, Interest Rate = 12%, Lender's Return = 8%, Number of Years = 8

This problem can't be properly solved without further clarifications.

3. Final Answer

Problem 1: Interest earned: $

9

0

0. Total amount: $

5

9

0

0. Problem 2: Total interest paid: $

4

8

0

0. Final amount to be repaid: $

1

6

8

0

0. Problem 3: Total amount: $3646.

5

2. Problem 4: Amount accumulated: $9511.

8

1. Problem 5: (i) Total amount: $164530.

8

9. Compound interest: $64530.

8

9. (ii) Total amount: $163861.

6

4. Compound interest: $63861.

6

4. Problem 6: Amount accumulated: $13954.

0

1. Problem 7: Sum of money available: $

1

5

2

6

2

7

5. Problem 8: Amount left after seven years: $1311.

8

8. Problem 9: Amount of each installment: $7188.

2

9. Problem 10: Amortization schedule cannot be prepared here.