Question

1. How do you calculate equal annual payment on a loan of $1 billion payable in 10 years a 10% interest rate(Engineering Mathematics)

– principal payment

–Total payment

– Annual payment

- Effective Interest payment

-Absolute

Answer 1

Loan = 1 B = 1000m

t = 10 yrs

i = 10%

Annual payments = 1000m * (A/P, 10%, 10) = 1000m * 0.162745 = 162.745 m

or

Annual payments = 1000 m * [ 0.10*((1 + 0.1)^10)/((1 + 0.1)^10-1)]

= 1000 m * [ 0.10*((1.1)^10)/((1.1)^10-1)]

= 1000m * .(0.1 * 2.593742) / (2.593742 - 1)

= 1000m * 0.162745 = 162.745 m

Total payment = 162.745 m * 10 = 1627.45m

Interest payment = 1627.45m - 1000m = 627.45m

interest payment in first annual payment = 1000m* 0.1 = 100m

Principal payment in first annual payment = 162.745 m - 100m = 62.745m