Question

1.

A couple has just purchased a home for $447,300.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 3.72% APR with monthly compounding. The mortgage has a term of 30 years.

How much interest is paid in the first year?

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2.

A professor has two daughters that he hopes will one day go to college. Currently, in-state students at the local University pay about $22,119.00 per year (all expenses included). Tuition will increase by 3.00% per year going forward. The professor's oldest daughter, Sam, will start college in 16 years, while his youngest daughter, Ellie, will begin in 18 years. The professor is saving for their college by putting money in a mutual fund that pays about 7.00% per year. Tuition payments are at the beginning of the year and college will take 4 years for each girl. (Sam's first tuition payment will be in exactly 16 years)

The professor has no illusion that the state lottery funded scholarship will still be around for his girls, so how much does he need to deposit each year in this mutual fund to successfully put each daughter through college. (ASSUME that the money stays invested during college and the professor will make his last deposit in the account when Sam, the OLDEST daughter, starts college.)

Answer 1

(1) Purchase Price = $ 447300, Cash Down Payment = 20 % = 0.2 x 447300 = $ 89460

, Mortgage = 447300 - 89460 = $ 357840

APR = 3.72 % with monthly compounding and Tenure = 30 years or 360 months

In order to determine the interest paid in Year 1, one needs to determine the mortgage amount outstanding at the end of Year 1, subtract the same from the original mortgage amount to arrive at the magnitude of mortgage repaid. This mortgage repaid when subtracted from the total equal monthly repayments of year 1 (only) will equal the interest paid on the mortgage in year 1.

Let the equal monthly repayments be $ P

Monthly Interest Rate = (3.72 / 12) = 0.31 %

357840 = P x (1/0.0031) x [1-{1/(1.0031)^(360)}]

P = $ 1651.127 ~ $ 1651.13

Total of Monthly Repayments for Year 1 = 12 x 1651.13 = $ 19813.53

Mortgage Outstanding at the end of Year 1 = PResent Value at the end of Year 1 of remaining monthly payments = 1651.13 x (1/0.0031) x [1-{1/(1.0031)^(348)}] = $ 351226.1

Mortgage Repaid in Year 1 = 357840 - 351226.1 = $ 6613.926 ~ $ 6613.93

Interest Paid in Year 1 = Total of Monthly Repayments - Mortgage Repaid in Year 1 = 19813.53 - 6613.93 = $ 13199.6

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with a maximum of four sub-parts.