Question

Plans for Repayment of $17,000 in Four Months with Interest at 1% Plan 2: Pay off the debt in four equal end-of-month installments (principal and interest). $17,000 $170 $17,170 $4,187.10 $4,357.10 12,812.90 128.13 12,941.03 4,228.97 4,357.10 8,583.93 85.84 8,669.77 4,271.26 4,357.10 4,312.67 43.13 4,355.80 4,313.97 4,357.10 42,709.5 $-mo. $427.10 (total interest) Difference = $1.30 due to roundoff- $0 Plan 3*: Pay principal and interest in one payment at end of fourth month. $17,000 $170 $17,170 17,170 171.70 17,341.70 17,341.70 173.42 17,515.12 17,515.12 175.15 17,690.27 69,026.8 $-mo. $690.27 (total interest) 17,000 17,690.27

Please explain from we get (4187.1) in plan 3 ..and all the numbers????

Answer 1

In plan 2,
The $17000 is repaid by 4 equal installments with 1% interest rate per period.

We need to calculate the payment amount here.
=PMT(1%,4,-17000)
= $4356.78

In 1st month,
Interest accrued is calculated by
$17000 * 0.01 = $170

The equated periodic payment is $4356.78
Principal payment = 4356.78 - 170
= $4186.78 or 4187

2nd month
New Principal = 17170 - 4356.78 = 12813.22
Interest = 12813.22 * 0.01 = 128.13
4356.78 - 128.13 = 4228.65

Thus, we can calculate for the 3rrd and 4th payment.

This is the amount paid each period for total of 4 periods.
4 * 4356.78 = 17427.11

The principal amount was $17000 so the total interest paid is $427.11
17427.11 - 17000 = $427.11

The interest paid should be equal.

In the plan 3,
The $17000 amount is repaid by only a single and final payment.
We will need to calculate only future value here.
FV = Amount*(1+Interest Rate)^Years

=FV(1%,4,,-17000)
= $17690.27

Again, the interest paid is calculated by
17690.27 - 17000 = 690.27

The interest paid in the plan 3 is higher because it involves a single payment. The plan 2 had an equated periodic payment which means the principal amount was reduced with each payment. It is not the case in plan 3.