Loan Repayments - Series And Sequence (1 Viewer)

[velox]

A $2000 loan is offered at 18% p.a. interest, charged monthly, over four years. If no repayments need to be paid for the first 3 months, find the amount of each repayment. How much will be paid back altogether?

 

[Xayma]

The amount is 1.015³*2000 and there are 45 payments. Otherwise it is a normal time payment.

 

[velox]

hmm answer says otherwise

 

[Xayma]

Well then the answers are wrong. . The only thing different would be if they did 48 payments but didnt start M till the 3rd.

T1=1.015*2000
T2=1.015²*2000
T3=1.015³*2000
T4=1.015⁴*2000-M
.
.
.
T48=1.015⁴⁸*2000-M(1+1.015+1.015²+....+1.015⁴⁵)

 

[Katie123]

I am going to probably have to skip that question or the majority of it IT is a LOST CAUSE

 

[Steven12]

dude, this is what i did, tell me if the answer confirms this

no repayments at for first three months and that includes interest i assume. so we being on the 4th month

4th month 2000*1.015-M where M is the monthly payment
5th (2000*1.015-M)1.015-M
2000*1.015^2-1.015M-M
sixth (2000*1.015^2-1.015m-m)1.015-m
2000*1.015^3-1.015M^2-1.015M-M

rearrange(sixth month) = 2000*1.015^3-M(1+1.015+1.015^2)
so the trend is 2000*1.015^(n-3)-M(1+1.015+1.015^2)

so on the 48th 2000*1.015(48-3)-M( 1(1.015^45-1)/ (1.015-1)=0
from that you can work out M=61.4 dollars

since there are 45 paying months 61.4*45=2763 dollars

Is this right? with your answer?