Obuor, a level 100 student at University of Ghana plans to take a student loan to finance his  four year PhD study at the university. He plans to take Ghc5000 for each  academic  year and this amount will attract an interest of 15 percent annually  compounded quarterly. How much will he owe the loan company after his four year study if he plans to take the loan at the start of each academic year?  Blank 1. Fill in the blank, read surrounding text.

To solve this problem, we need to understand the concept of compound interest and how it is calculated. Compound interest is calculated on the initial principal, which includes all of the accumulated interest of previous periods of a deposit or loan.

The formula for compound interest is:

A = P (1 + r/n) ^ nt

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested or borrowed for, in years.

Given that Obuor is taking a loan of Ghc5000 every year for four years, and the interest rate is 15% compounded quarterly, we need to calculate the total amount he will owe for each year's loan and then sum them up.

1. For the first year's loan of Ghc5000, it will compound for 4 years.
2. For the second year's loan of Ghc5000, it will compound for 3 years.
3. For the third year's loan of Ghc5000, it will compound for 2 years.
4. For the fourth year's loan of Ghc5000, it will compound for 1 year.

Let's calculate:

1. A1 = 5000 (1 + 0.15/4) ^ (4*4) = Ghc7456.42
2. A2 = 5000 (1 + 0.15/4) ^ (4*3) = Ghc6488.89
3. A3 = 5000 (1 + 0.15/4) ^ (4*2) = Ghc5643.86
4. A4 = 5000 (1 + 0.15/4) ^ (4*1) = Ghc4882.83

Adding all these amounts together, Obuor will owe the loan company Ghc23471.99 after his four year study.

To solve this problem, we need to understand the concept of compound interest and how it is applied annually.

Step 1: Understand the problem Obuor is taking a loan of Ghc5000 every year for four years. The interest on the loan is 15% compounded quarterly. We need to find out how much he will owe at the end of four years.

Step 2: Calculate the quarterly interest rate The annual interest rate is 15%, but it is compounded quarterly. So, we divide the annual interest rate by 4 to get the quarterly interest rate. 15% / 4 = 3.75%

Step 3: Calculate the compound interest for each year The formula for compound interest is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

We apply this formula for each year separately because the loan is taken at the start of each academic year.

Year 1: A1 = 5000(1 + 0.0375/4)^(41) = Ghc5439.56 Year 2: A2 = 5000(1 + 0.0375/4)^(42) = Ghc5912.28 Year 3: A3 = 5000(1 + 0.0375/4)^(43) = Ghc6422.71 Year 4: A4 = 5000(1 + 0.0375/4)^(44) = Ghc6973.68

Step 4: Calculate the total amount owed The total amount owed is the sum of the compound interest for each year. Total = A1 + A2 + A3 + A4 = Ghc5439.56 + Ghc5912.28 + Ghc6422.71 + Ghc6973.68 = Ghc24748.23

So, Obuor will owe the loan company Ghc24748.23 after his four-year study.