mathematicsoffinance数学题求解1.1.Mrs.SinghowesMr.Valdy$55,513.78in14-months.Mr.Valdyagreestoletherrepaytheloanwithapaymentof$35,000in6-months,$10,000in8-monthsand$Xin14-months.Ifmoneyisworthj4=6%,whatistheval

Question

mathematics of finance数学题求解
1.1.Mrs.Singh owes Mr.Valdy $55,513.78 in 14-months.Mr.Valdy agrees to let her repay the loan with a payment of $35,000 in 6-months,$10,000 in 8-months and $X in 14-months.If money is worth j4 = 6%,what is the value of X,using 14-months as the focal date along with the exact method of crediting/charging interest?
2.2.A car insurance company charges you a premium of $1452 a year for your car insurance policy.You have two options.Option 1 is to pay the $1452 in cash today.Option 2 is to make three payments of $499 at the following times:today,3-months from now and 6-months from now.What nominal rate of interest,j4,are you being charged?

Answer 1

1.1 X={[(55513.78*(1+j)^6-35000]*(1+J)^2-10000}*(1+J)^6=12800.08 （j=0.5%）
1.2 according the question factor establish the equation 1452*(1+j)^6=499*[(1+j)^6+(1+j)^3+1],
replace (1+j)^3 with r,therefore:(1452-499)*r^2-499*r-499=0,
the solution for above equation is r=1.031318583,
hence j=r^(1/3)-1=1.0103324-1=0.010,
thus we can get nominal rate of interest j4=12*j=0.12≈12%.