This is a tricky problem . . .Tom borrowed a sum of money at 10% per annum compound interest.
If he repaid the sum only after 2 years, he would have to repay $4356.
I already found the sum of money that he had borrowed to be $3600. Yes!
If he repaid the sum by two equal annual installments,
at the end of the first year and the second year,
how much was each installment?
It is an Amortization problem (time payments).
There is a formula for this situaton, but we can derive it ourselves.
Tom owes $3600. .The bank charges 10% interest per year.
. . Let = amount of his two equal payments.
During the first year, the bank charges 10% interest: .
. . At the end of year one, Tom owes: . dollars.
Then Tom pays dollars.
. . So he owes a balance of dollars.
During the second year, the bank charges 10% interest: .
. . At the end of year two, Tom owes: . dollars
Then Tom pays dollars and he owes $0.
. . [His last balance is equal to his final payment.]