Suppose you won the lottery of $325,000 with 75,000 paid up front and 50,000 paid at the end of each year.?

Question

If the interet rate is 6.25%. What is the actual amount of money won.

I am trying to learn technical side of finance on my own, so if you can explain how you got the answer in simple terms that would be great.

I would also like to know how to figure out what the total amount owed on a loan of $216.36 to be paid at the end of 6yrs at 7.5% interest.

Thanks

Answer 1

You would win 325,000 the question to me seems to be asking what is the time it takes for the payout of the whole 325,000

In that case you have:

PV=325000-75000=250000

i=6.25

PMT= -50000

FV=0

therefore

n=7 years

As for your second question

PV=216.36

i=7.5

n=6

therefore

FV= 333.91

Answer 2

325000-75K=250K (75K won)

250K x 1.0625=265625

265625-50K=215625(125K won)

215625 x 1.0625=229101.56

229101.56-50K=179101.56(175K won)

179101.56 x 1.0625=190295.41

190295.41-50K=140295.41(225K won)

140295.41 x 1.0625=149063.87

149063.87-50K=99063.87 (275K won)

99063.87 x 1.0625=105255.37

105255.37-50K=55255.37 (325K won)

55255.37 x 1.0625=58,708.83

58,708.83 -50K=8,708.83 (375K won)

8708.83 x 1.0625=9253.13

9253.13 - 9253.13=0 (384,253.13 won, 59,253.13 of it was interest, and the party is over!)

the second question is much less laborious:

216.36 x 1.075^6 = 333.91

(the logic here is 6 years of compounded interest on the full amount of the loan is calculated by multiplying it times 1.075, then multiplying THAT, the total with first years interest, by the same interest for year two, and so on.