Paul takes a loan of 225000 from the bank at 7 interest rate

Paul takes a loan of $225,000 from the bank at 7% interest rate per year over a 10-year period. He plans to pay off the loan in 10 yearly payments of $16,000 each, and with the money that he is going to inherit from his grand parents. How much should he inherit to pay off the entire loan if the grand parents give him the money at the end of the 4th year and he hands over the entire amount to the bank on the day he receives it?

Solution

Year 0 $225,000 Interest rate 7% Repayment $ 16000/year in 10 years + Money inherited from grandparents (Amount in $) Year Year beginning Interest @ 7% for one year Loan + Interest Repayment Yead end balance 1                   225,000                   15,750          240,750 16,000                         224,750 2                   224,750                   15,733          240,483                   16,000                         224,483 3                   224,483                   15,714          240,196                   16,000                         224,196 4                   224,196                   15,694          239,890                   16,000                         223,890 5                   223,890                   15,672          239,562                   16,000                         223,562 6                   223,562                   15,649          239,212                   16,000                         223,212 7                   223,212                   15,625          238,836                   16,000                         222,836 8                   222,836                   15,599          238,435                   16,000                         222,435 9                   222,435                   15,570          238,006                   16,000                         222,006 10                   222,006                   15,540          237,546                   16,000                         221,546 The year-end balance shown in the table corresponding to each year is the amount required to close the loan at the end of respective year So Paul should inherit from his grandparents $ 223,890 to pay off the entire loan at the end of 4th year