Question

Andres Michael bought a new boat. He took out a loan for S24 320 at 45% interest for 2 years. He made a 54.110 partial payment at 2 months and another partial payment of $3.410 at 6 months. How much is due at maturity? (Do not round intermediate calculations

Answer 1

$25,381.94

Explanation:

45% interest in 2 years = 45/24 = 1.875% monthly

Debt at month 0 (when Andres got the loan)

24,320

Debt at month 1

24,320*(1 + 0.001875) = 24,365.6

Debt at month 2

24,365.6*(1.001875) - 54.110 (partial payment) = 24,357.1755

Debt at month 3

24,357.1755*(1.001875)

Debt at month 4

`24,357.1755*(1.001875)^2`

Debt at month 5

`24,357.1755*(1.001875)^3`

Debt at month 6

`24,357.1755*(1.001875)^4` - 3,410 (partial payment)

= 24,540.36874

Debt at month 7

24,540.36874*(1.001875)

Debt at month 8

`24,540.36874*(1.001875)^2`

Debt at month 9

`24,540.36874*(1.001875)^3`

and so on until month 24 (the maturity)

Debt at maturity

`24,540.36874*(1.001875)^(18)`

= 25,381.93916 = $25,381.94 rounded to the nearest hundreth.