Question

Derek borrows $276,041.00 to buy a house. He has a 30-year mortgage with a rate of 4.03%. The monthly mortgage payment is $________.

Answer format: Currency: Round to: 2 decimal places.

Suppose you deposit $1,104.00 into an account 6.00 years from today. Exactly 14.00 years from today the account is worth $1,476.00. What was the account's interest rate?

Answer format: Percentage Round to: 3 decimal places (Example: 9.243%, % sign required. Will accept decimal format rounded to 5 decimal places (ex: 0.09243))

Answer 1

Derek borrows $276,041.00 to buy a house. He has a 30-year mortgage with a rate of 4.03%.

PV = 276,041

n = 30 * 12 = 360 monthly payments

r = 4.03%/12 = 0.003358333333 monthly rate

The monthly mortgage payment is $1,322.64

Suppose you deposit $1,104.00 into an account 6.00 years from today. Exactly 14.00 years from today the account is worth $1,476.00.

PV6 = 1,104

FV14 = 1,476

Number of years, n = 14 - 6 = 8

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

(1 + r) = (FV/PV)^(1/n)

1 + r = (FV/PV)^(1/n) - 1

r = (FV/PV)^(1/n) - 1

r = (1,476/1,104)^(1/8) - 1

r = 1.3369565217^(1/8) - 1

r = 1.0369663427 - 1

r = 0.0369663427

r = 3.697%

Account's interest rate was 3.697%

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