Question

You are taking a €2000 loan. You will pay it back in four equal amounts, paid every 6 months starting 3 years from now. The interest rate is 6% compounded semiannually. Calculate the amount of each payment.

Answer 1

€623.03

Step-by-step explanation:

semiannually = 2

€2000 x (1 + 0.03/2)^(6) ≈ €2492.11 €2492.11 ÷ 4 = €623.03

FV = PV x (1 + r/2)^(n x 2)

FV = Future Value (€2492.11)

PV = Present Value (€2000)

r = Interest Rate (6%/2 = 3%)

n = Number of periods (3 years x 2 = 6 periods)

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Answer 2

To find the amount of each semiannual payment for the loan, we use the present value of annuities formula, adjusting for the interest rate and the number of payments, allowing us to solve for the regular payment amount.

Step-by-step explanation:

To calculate the amount of each payment for a €2000 loan with a semiannual repayment schedule starting 3 years from now at a 6% interest rate compounded semiannually, we can use the present value of annuities formula. This involves discounting the future payments back to their present value and solving for the regular payment amount (R). The formula is:

`PV = R * [(1 - (1 + i)^(-n)) / i]`, where PV is the present value of the loan, i is the interest rate per period, and n is the total number of payments.

First, we calculate the interest rate per period: i = 6% / 2 = 0.03 per semiannual period. As the payments start 3 years or 6 periods from now, the number of payments n is 4.

Using the formula, we have:

`2000 = R * [(1 - (1 + 0.03)^(-4))` / 0.03]

Rearranging the formula to solve for R, we get:

`R = 2000 / [(1 - (1 + 0.03)^(-4)) / 0.03]`

By calculating the expression inside the square brackets, we find the sum of the discount factors for each payment, and then divide the loan amount by this sum to find the value of R, which is the amount of each payment.