



 
Hi Robin. Let's write out the first few years to examine the pattern closely:
The cumulative payment total (CPT) is the previous CPT + the fixed payment + the interest for the current year. The interest for year n is the balance carried forward times 5%. The balance carried forward for year n is $3 000 000 minus $150 000 times n. So CPT(n) = CPT(n1) + 150 000 + 0.05 * (3 000 000  150 000n). Another way of writing this is by using summation. Remember that a sum of a sum is a sum, so we can simplify the summation in steps: Now the remaining summation is just the sum of the first few natural numbers. This is a wellknown sum: the sum of the first A natural numbers is equal to A(A+1)/2, so we complete the problem as follows: There's the result. A total of $4 425 000 would be paid out.  


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