Question

Sam Robinson borrowed $11,000 from a friend and promised to pay the loan in 10 equal annual installments beginning one year from the date of the loan. Sam’s friend would like to be reimbursed for the time value of money at a 10% annual rate. What is the annual payment Sam must make to pay back his friend? (Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.)

Answer 1

Answer:

P = $1790.01

Explanation:

Given data:

Borrowed money = $11,000

Number of installment = 10

Annual rate of interest = 10%

$11,000 = P(1.1)^1 + P(1.1)^2 + P(1.1)^3 + P(1.1)^4 + P(1.1)^5 + P(1.1)^6 + P(1.1)^7 + P(1.1)^8 + P(1.1)^9 + P(1.1)^10$

$\frac{11,000}{17.53} = P$

P = $627.45

PV of annuity is given as:

$PV of annuity = P*[\frac{(1-(1+r)^{-n})}{ r}]$

P - Periodic payment

r - rate per period

n - number of periods

$11,000 = P*[\frac{(1-(1+0.1)^{-10})}{0.1}]$

P = $1790.01