Question

Damien McCoy has loaned money to his brother at an interest rate of 5.85 percent. He expects to receive $987, $1,012, $1,062, and $1,162 at the end of the next four years as complete repayment of the loan with interest. How much did he loan out to his brother? (Round to the nearest dollar.)

Damien McCoy has loaned money to his brother at an

a.$3,657
b.$3,685
c.$3,785
d.$3,757

Answer 1

correct option is a.$3,657

Step-by-step explanation:

given data

interest rate = 5.85 percent

cash c1 = $987

cash c2 = $1,012

cash c3 = $1,062

cash c4 = $1,162

solution

we get here loan amount in 4 year that is express as

loan amount =
`(c1)/((1+r)) +(c2)/((1+r)^2) +(c3)/((1+r)^3) +(c4)/((1+r)^4)` .........................1

put here value and we get

loan amount =
`(987)/((1+0.0585)) +(1012)/((1+0.0585)^2) +(1062)/((1+0.0585)^3) +(1162)/((1+0.0585)^4)`

solve it we get

loan amount = 3656.79

loam amount = $3657

so correct option is a.$3,657