A 30-year loan of $1,000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each of the next 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

X = $374.16

Step-by-step explanation:

First we have to calculate for the amount of interest using compound interest formula

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

P (principal) = 1000

r (rate) = 10% = 0.1

t (time in year) = 30

n (number of recursion per year) = 1

A = 1000 (1 + (0.1/1)) ^ (1*30) = 17,449.40

Amount of compound interest for 30 years is

I = A - P = 17,449.40 - 1000 = 16,449.40

Amount of interest due per year

= I/30

= 16,449.40/30 = 548.313

The guy paid the same amount of interest due for the first 10 years

548.313*10 = 5483.13

And the next 10 payments equal to 150% of the interest due (150% = 1.5 times)

548.313*10*1.5 = 8224.7

Total of paid interest is

8224.7 + 5483.13 = 13707.83

So, the balance unpaid loan is

17449.40 - 13707.83 = 3741.57

This balance payment is dividend for the last 10 years, so

3741.57/10 = 374.16

So X = $374.16