Question

Ian loans Yifan $600. Yifan repays the loan by paying $310 at the end of two and a half years and $325 at the end of four years. The money which Ian receives at the end of two and a half years is immediately reinvested at an annual effective interest rate of 4%. Find Ian’s annual effective rate of interest and Yifan’s annual yield.

The answers are 2.16941% and 1.75280% respectively. Just need the work to show how to find these

Answer 1

Yifan		1.50%			2%
		NPV@ 0.015			PV@ 0.02
Year	Cash flow	PV factor	PV-Cash flow		PV factor	PV-Cash flow
0	(600.00)	1.000	(600.00)		1.000	(600.00)
2.5	310.00	0.963	298.67		0.952	295.03
4	325.00	0.942	306.21		0.924	300.25
		Total PV	4.88		Total FV	(4.72)
	IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
		'=0.015+ (0.02-0.015)*(4.8833/(4.8833-(-4.723)
		1.7542%
Ian
Amount rec at T2.5	310.00
Investment rate	4%
Amount at T4	310*(1+4%)^1.5
Amount at T4	328.78
Amt rec at t4 from Yifen	325.00
Total Amount	653.78
Initial amount	600.00
653.78=	600*(1+r)^4
(1+r)^4	653.78/600
(1+r)^4	1.089633
1+r	=1.08963^(1/4)
1+r	1.021691
r=	0.021691
r=	2.169%