Dax borrows $300,000 and the loan is governed by compound interest at an annual effective interest rate of 4.75%. Dax agrees to repay the loan in ten equally spaced payments, the first four of which are for $21,000 and the next six of which are for $41,000. The first payment should therefore be made in 73.944 days.
The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
The equal spacing of the payments is a given. The timeline of the supplied cash stream would look like this if the first payment were made t years from now.
Thus, the first payment will be made in t years, the second in 2t years, and so on.
To determine the value of t, multiply the present value of each of the 10 payments by the $300,000 original loan amount.
Total present value = 300,000
Total Future Value =21,000 * 4 + 41,000 * 6 = 84,000 + 246,000 = 330,000
Interest rate = 4.75%
So, now we calculate the nper using = nper(rate,pmt,pv,fv) =nper(0.0475,0,-300000,330000) = 2.054 Years
So, number of days = 2.054 * 360 = 739..44/10 = 73.944 days (Rounded to 3 decimal places)
So, the first payment can be made in 73.944 days (74 days) or 2 months and 14 days
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