Question

Sam promises to pay Sandy $2,000 in four years and another $3,000 four years later for a loan of $2,000 from Sandy today. What is the interest rate that Sandy is getting? Assume interest is compounded monthly. A. 14.75% B. 16.72% C. 15.10% D. 18.08%

Answer 1

Answer:

the interest rate that Sandy is getting is (C.) 15.10%

Explanation:

Given data

in 4 year cash pay (p1)  = $2000

in 8 year cash pay (p2)  = $3000

time period (t1) = 4 years

time period (t2) =  8 years

loan value = $2000

To find out

interest rate

solution

first we know amount will be paid in first 4 year is

$2000 $(1+r/100)^{12t}$

$2000 $(1+r/100)^{48}$                  ...................1

now we calculate the next payment will paid after 4 year i.e.

$2000 $(1+r/100)^{12t}$ - $2000  

$2000 $(1+r/100)^{48}$   - $2000  ..................2

after full time period of payment total amount will be paid by equation 1 and 2  i.e.

$3000 = $2000 $(1+r/100)^{48}$ ×$2000 $(1+r/100)^{48}$ - $2000

$3000 = $2000 ( $(1+r/100)^{48}$ ×  $(1+r/100)^{48}$ - 1 )   .....3

now we have solve   $(1+r/100)^{48}$ this eqution

so we consider  $(1+r/100)^{48}$ = A

so new equation will be by equation 3

$3000/$2000 = ( A - 1 ) × A

3/2 = A² - A

solve this equation we get  2A² - 2 A - 3 = 0 so A = 1.823

now we compute A again in  $(1+r/100)^{48}$ = A

$(1+r/100)^{48}$ = 1.823

so rate (r) = 1.258 % / month

and rate yearly = 1.258 ×12

the interest rate that Sandy is getting yearly 15.10 %