# quiz5 $There~is~an~arithmetic~series,~1,~4,~7,~10~...~Find~the~sum~of~first~20~terms.$ $There~is~a~geometric~series,~3,~6,~12,~24~...~Find~the~sum~of~first~10~terms.$ $There~is~a~geometric~series,~100,~50,~25,~12.5~...~Find~the~sum~of~infinite~number~of~terms.~$ $If~100~GBP~is~invested~at~5%~p.a.,~what~will~be~the~total~sum~of~the~principal~and~interest~5~years~later,~in~case~of~simple~interest?$ $If~100~GBP~is~invested~at~5%~p.a.,~what~will~be~the~total~sum~of~the~principal~and~interest~5~years~later,~in~case~of~compound~interest?~Hint:~1.05^{5}\simeq1.276~$ $If~a~economy~grows~at~3%~p.a.,~how~much~will~be~the~cumulative~GDP~growth~rate(in~%)~in~ten~years?~Hint:~1.03^{10}\simeq1.344~$ $The~population~of~a~city~is~1,000,000~now.~The~population~grows~at~1.5%~per~year.~What~will~be~the~population~of~the~city~20~years~later?$ $What~is~the~future~compound~value~of~100~GBP~invested~for~20~years~at~10%~p.a.?$ $If~100~GBP~is~invested~at~10%~p.a,~but~interest~is~paid~four~times~a~year~(compound~interest).What~will~be~the~sum~of~principal~and~interest~one~year~later?~$ $~Hint:~1.025^{4}\simeq1.104$ $What~is~the~effective~annual~interest~rate~(or~APR)~when~the~nominal~annual~rate~is~10%~and~interest~is~paid~monthly?$ $If~100~GBP~is~invested~at~10%~p.a,~and~interest~is~paid~four~times~a~year~(compound~interest),~what~will~be~the~future~value~(sum~of~principal~and~interest)~$ $10~years~later?$ $The~interest~rate~is~5%~p.a.~and~there~in~no~credit~constraint~-~I~can~freely~borrow~and~lend~at~5%~p.a.~without~any~limit.~What~is~the~PV~(present~discounted~value)~$ $of~receiving~1000~GBP~20~years~later?$ $Which~of~the~following~investments~provides~the~best~rate~of~return?$ $For~which~of~the~following~examples,~is~the~PV~largest?$ $Find~the~combined~PV~of~the~future~payments,~500~GBP~in~one~year,~1000~GBP~in~3~years,~700~GBP~in~5~years.~Discount~rate~(interest~rate)~is~5%~p.a.~~$ $If~there~is~a~bond~which~pays~50~GBP~per~year~forever,~what~is~the~PV~of~this~bond?~The~interest~rate~is~4%~p.a.$ $There~is~a~bond~which~pays~100~GBP~every~year.~The~payment~will~begin~5~years~later,~and~will~continue~forever.~What~is~the~PV~of~this~bond?$ $There~is~a~bond~which~pays~50~GBP~for~5~years~from~now,~then~30~GBP~for~5~years~afterward.~What~is~the~PV~of~this~bond?~Discount~rate~is~5%~p.a.$ $If~you~invest~1000~GBP~now,~and~500~GBP~5~years~later,~what~will~be~the~total~wealth~(Future~value)~10~years~later?~The~interest~rate~is~5%~p.a.$
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