The current rates for an 80/20 mortgages are 4.15% for the first mortgages and 9.75% for the second mortgage. On a $200,000 30 y
1 answer:
Answer: The actual rate of the mortgage is 5.27%.
Since we're taking two mortgages for a total of $200,000 for 30 years, we can find the actual rate of the mortgage by finding the weighted average of the two rates. The weights in this case will be the proportion of loan taken at each rate
We have
Rates Weights Rates * Weights
4.15 0.80
9.75 0.20
Total 5.27%
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Answer:
1276.5
Explanation:
Today, Eric deposited an amount(PO) that is = 1000
The annual nominal Interest rate for the first 7 years = i
This is convertible semiannually.
As such,
The semi-annual interest rate for first 7 years =
The number of semi-annual periods in 7 years (k) = 2*7 = 14
The magnitude of the deposit at end of year 7( P7),
= P7 == P0 * (1 + i/2)14 ------ equation 1
On the other hand,
The nominal interest rate after 7 years = 2i which is convertible quarterly
The effective quarterly interest rate = =
The number of quarters between the end of year 7 and year 10.5 = 4* (10.5 - 7) = 14
The amount of deposit at the end of year 10.5 year = P10.5
=
* (1 +
---equation 2
We are given the following:
=1980
We shall thus substitute this value into the equation as
1980 = *( 1 + i/2)14
Further, we have worked out that
P7 == P0 * (1- i/2)14 *(1
We shall therefore substitute equation 1 into equation 2 as follows
1980 = P0 * (1+ i/2)14 *( 1 + i/2)14
1980 = 1000* (1+ i/2)14 *( 1 + i/2)14
This can also be rewritten as
1000* (1+ i/2)14 *( 1 + i/2)14 =1980
(1+ i/2)14 *( 1 + i/2)14 =1980/1000
(1+ i/2)28 =1.98
(1+ i/2) = 1.981/28
(1+ i/2) = 1.0247
i/2 = 1.0247 -1
i/2 = 0.0247
1 = 0.0247 *2 =0.0494
At the end of year 5, the amount has accumulated to an amount = X
X = Po * ( 1 + i/2 )10
= 1000 * ( 1 + 0.0494/2)10
= 1000 * ( 1 + 0.0247)10
= 1000 + ( 1.0247)10
= 1000* 1.276467
= 1276.5