Question

An amount of $2450 is borrowed for two years at a rate of 6.1% compounded continuously. Payments of $1000 each are made in six months and one year, determine the amount needed to settle the loan at the end of the term.

Please please please show work. I am struggling to figure out why my multiplication with e^x is never coming out calculated correctly.

Answer 1

EAR =[ e^(Annual percentage rate) -1]*100

6.1=(e^(APR%/100)-1)*100

APR% = 5.9212

Future value = present value*(1+ rate)^time

2450 = Present value*(1+0.059212)^2

Present value = 2183.7368

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

5.9212 = ((1+Stated rate%/(2*100))^2-1)*100

Stated rate% = 5.8361

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 1000*((1-(1+ 5.8361/200)^(-1*2))/(5.8361/200))

PV = 1915.7445

Remaining PV = 2183.7368-1915.7445

=267.9923

Future value = present value*(1+ rate)^time

Future value = 267.9923*(1+0.059212)^2

Future value = 300.67