📘 finance

1. **Problem Statement:** We need to find the value of $X$ given a timeline with cash flows at different times and a 5% interest rate. 2. **Understanding the Problem:** The timelin

1. **Problem Statement:** Calculate the discounted mean term (also called the Macaulay duration) of a bond redeemable at par in 10 years with annual coupons of 8%, at interest rate

1. **Problem Statement:** A firm plans to redeem Rs.50,00,000 of 12% debentures trading at 95% of face value and replace them with new 10% debentures issued at 98% of face value. T

1. **Problem Statement:** A company plans to invest 600,000 in drying equipment with a 5-year life and no salvage value. Cash inflows before tax are given for each year. The tax ra

1. **State the problem:** We need to find the discounted value of payments of 1012 made every six months for 8 years, with an interest rate of 5% per annum compounded quarterly. 2.

1. **State the problem:** We need to find the future value of an ordinary annuity with periodic payment $2160$, payment interval 1 month, term 3 years, interest rate 10% per year,

1. **State the problem:** We need to find the future value of an ordinary annuity with the following details: - Periodic payment: 4100

1. **State the problem:** We need to find the finance charge and the monthly payment to amortize a loan of 5400 with an annual interest rate of 13% over 48 monthly payments using t

1. **Problem Statement:** We are given zero coupon bond prices for different maturities and asked to calculate the 10-year yield to maturity ($Y_{10}$) and the 5-year forward rate

1. **Stating the problem:** Calculate the amount and compound interest for a principal sum after a certain time period with a given interest rate compounded annually. 2. **Formula

1. **State the problem:** We are given the spot rate function $$s(n) = 0.09 - 0.03e^{-0.1n}$$ and asked to find the one-year forward rate at time 10, denoted as $$f(10,11)$$. 2. **

1. **Problem statement:** A man borrows 5400 and repays 300 per month plus 1.5% interest on the unpaid balance each month. Find the total cost of the loan over 18 months. 2. **Unde

1. **State the problem:** We need to find the deposit (principal) that will earn $45.18 in interest over 240 days at an interest rate of 3.25% per year using simple interest. 2. **

1. **State the problem:** We need to find the principal amount that will earn 176.42 in interest at an annual simple interest rate of 4.75% over 8 months. 2. **Formula for simple i

1. **State the problem:** We need to find the total value of the car including the price change to Canada and insurance cost. 2. **Calculate the total value:**

1. **State the problem:** Calculate the tax free income, taxable income, annual income tax, monthly tax, and percentage of income paid as tax for a director earning 18000 with give

1. **Problem Statement:** Calculate the return and risk (standard deviation) of each stock ALI, TEN, and BOC from 2016 to 2024. 2. **Formula for Return:** The annual return $R_t$ f

1. **State the problem:** We need to find the weight of asset X in portfolio A. 2. **Formula:** The weight of an asset in a portfolio is given by

1. **Problem statement:** Jack opens an account with an initial deposit of 500000 Frw and deposits the same amount at the beginning of every year. The bank pays compound interest a

1. **State the problem:** We have a refrigerator priced at 1499 with a 12% interest rate over 18 months, a 6% discount, and a 20% down payment. We need to find the discount price,

1. **State the problem:** Gether borrows 27000 and pays 2832.18 interest at 2% annual interest compounded quarterly. We need to find the length of the loan in years. 2. **Formula:*