Question

Benjamin and St´ephanie’s mother/mother-in-law, Suzy, issued a $1 000 000 twenty-five year interest-only loan to the couple. Under the terms of the loan, they make annual payments of interest every year (at 3% p.a.); the final payment will consist of the regular interest amount together with the return of principal. Unbeknownst to the couple, Suzy has invested each interest payment at 3.5% p.a. Her intention is to give the accumulated amount to the couple when the loan matures. Allowing for this gift, what is Benjamin and St´ephanie’s net payment to Suzy when the loan matures? Include in your answer

• a fully labelled cash flow diagram (drawn from the perspective of Suzy’s investment fund),

• your chosen valuation date and

• an equation of value.

Please handwritten answer using formulas. Thank you so much.

Answer 1

Cash flow Time-line
For Benjamin and Stephanie’s				For Suzy's investment
Interest =1000000*3%=30000			1	2	3=Prev. bal.in 4*3.5%	4=prev.bal.in 4+Current (2+3)
End of Year	Cash outflow(to Suzy)		EOY	Amt. Invested	Interest at 3.5%p.a.	Bal.in a/c
1	-30000		1	30000	0	30000
2	-30000		2	30000	1050	61050
3	-30000		3	30000	2137	93187
4	-30000		4	30000	3262	126448
5	-30000		5	30000	4426	160874
6	-30000		6	30000	5631	196505
7	-30000		7	30000	6878	233382
8	-30000		8	30000	8168	271551
9	-30000		9	30000	9504	311055
10	-30000		10	30000	10887	351942
11	-30000		11	30000	12318	394260
12	-30000		12	30000	13799	438059
13	-30000		13	30000	15332	483391
14	-30000		14	30000	16919	530310
15	-30000		15	30000	18561	578870
16	-30000		16	30000	20260	629131
17	-30000		17	30000	22020	681150
18	-30000		18	30000	23840	734991
19	-30000		19	30000	25725	790715
20	-30000		20	30000	27675	848390
21	-30000		21	30000	29694	908084
22	-30000		22	30000	31783	969867
23	-30000		23	30000	33945	1033812
24	-30000		24	30000	36183	1099996
25	-1030000		25	30000	38500	1168496

So, from the above , we can infer that

Benjamin and Stephanie’s net payment to Suzy when the loan matures

will be -1000000+(-30000)+1168496=

138496

Cash Inflow from Suzy to Benjamin & Stephanie

Suzy' s accumulation can also be calculated

by using the Future value of ordinary (year-end) annuity formula,

FVOA=Pmt.*(1+r)^n-1)/r

Where,

FVOA needs to be found out--??

Pmt.=the annual investment into the account, ie. $ 30000

r= rate of interest, ie. 3.5% p.a.

n=no.of compounding periods, ie. 25

so, plugging the values, we have,

FVOA=30000*((1+0.035)^25-1)/0.035=

1168495.701

So, forming an equation with the numbers for the last payment , at end of 25 years,

Benjamin and Stephanie’s net payment to Suzy when the loan matures

will be -1000000+(-30000)+1168496=

138496

which is Cash Inflow from Suzy to Benjamin & Stephanie

as her gift