A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X.

Step-by-step explanation:

Given

--- time (years)

--- amount

--- rate of interest

Required

The last 10 payments (x)

First, calculate the end of year 1 payment

Amount at end of year 1

Rewrite as:

Next, calculate the end of year 1 payment

Amount at end of year 2

Rewrite as:

We have been able to create a pattern:

So, the payment till the end of the 10th year is:

To calculate X (the last 10 payments), we make use of the following geometric series:

The amount to be paid is:

--- i.e. amount at the end of the 10th year * rate of 10 years

So, we have:

The geometric sum can be rewritten using the following formula:

In this case:

So, we have:

So, the equation becomes:

Solve for x

Approximate

step-by-step explanation:

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