# Why is this true in this series???

• Jun 5th 2006, 12:08 AM
nath_quam
Why is this true in this series???
Tarzan and Jane borrow \$B to buy a jungle condomium at an interest rate of 9.6% pa, compounded monthly. They borrow the money on 15th September, and on the 14th day of every subsequent month, they pay an instalement of \$M. Let An be the amount owing after n months have passed

Explain why A1 = 1.008 x B - M and why A(n-1) = 1.008An - M for n >= 2

Thanks for any help
• Jun 5th 2006, 12:18 AM
CaptainBlack
Quote:

Originally Posted by nath_quam
Tarzan and Jane borrow \$B to buy a jungle condomium at an interest rate of 9.6% pa, compounded monthly. They borrow the money on 15th September, and on the 14th day of every subsequent month, they pay an instalement of \$M. Let An be the amount owing after n months have passed

Explain why A1 = 1.008 x B - M and why A(n-1) = 1.008An - M for n >= 2

Thanks for any help

9.6% pa compounded monthly means a rate of 9.6/12% pm = 0.8% pm.

From there the rest should be simpel enough.

RonL
• Jun 5th 2006, 12:28 AM
nath_quam
Thanks i know that but how does that help prove the two statements
• Jun 5th 2006, 01:24 AM
CaptainBlack
Quote:

Originally Posted by nath_quam
Thanks i know that but how does that help prove the two statements

If the amount owed at the start of a month is D, then at the end of the
month 0.008D intrest has accrued, and you have paid off M, so you are left
owing:

D'=1.008D-M.

To obtain the given relations just plugin the debt at the start of the
relevany months.

RonL
• Jun 5th 2006, 01:26 AM
CaptainBlack
Quote:

Originally Posted by nath_quam
Tarzan and Jane borrow \$B to buy a jungle condomium at an interest rate of 9.6% pa, compounded monthly. They borrow the money on 15th September, and on the 14th day of every subsequent month, they pay an instalement of \$M. Let An be the amount owing after n months have passed

Explain why A1 = 1.008 x B - M and why A(n-1) = 1.008An - M for n >= 2

Thanks for any help

Don't post the same question twice.

RonL