Question Summary :

Multiple questions on use of time value of money

Answer 1 :

Given : Loan amount of 78400 $

Instalment of Rs 8500 $ at the enfd of each year

Interest rate 7.5%

  

By paying $8,500.00 every year, the loan will be paid off in 16 years and 3.3 months.

Total of 17 Loan Payments	$138,322.58
Interest	$59,922.58

Using the Amortization Schedule in Excel made through PMT, IPMT and PPMT functions : Amortization Schedule

	Beginning Balance	Interest	Principal	Ending Balance
1	$78,400.00	$5,880.00	-$2,620.00	$75,780.00
2	$75,780.00	$5,683.50	-$2,816.50	$72,963.50
3	$72,963.50	$5,472.26	-$3,027.74	$69,935.76
4	$69,935.76	$5,245.18	-$3,254.82	$66,680.94
5	$66,680.94	$5,001.07	-$3,498.93	$63,182.02
6	$63,182.02	$4,738.65	-$3,761.35	$59,420.67
7	$59,420.67	$4,456.55	-$4,043.45	$55,377.22
8	$55,377.22	$4,153.29	-$4,346.71	$51,030.51
9	$51,030.51	$3,827.29	-$4,672.71	$46,357.80
10	$46,357.80	$3,476.83	-$5,023.17	$41,334.63
11	$41,334.63	$3,100.10	-$5,399.90	$35,934.73
12	$35,934.73	$2,695.10	-$5,804.90	$30,129.83
13	$30,129.83	$2,259.74	-$6,240.26	$23,889.57
14	$23,889.57	$1,791.72	-$6,708.28	$17,181.29
15	$17,181.29	$1,288.60	-$7,211.40	$9,969.88
16	$9,969.88	$747.74	-$7,752.26	$2,217.63
17 (Partial)	$2,217.63	$166.32	$2,217.63	$0.00

Hence last instament of $ 2217 is to be repaid

Answer 2

Given : Interest rate 7.25% compounded monthly

Term : 8 years

Annuity : 395 at the end of each 6 months

PV of Ordinary Annuity?=C × [1−(1+i) ^ −n?]? / i

Present Value (PV) of the Ordinary Annuity

$ 4,713.17

Answer 3 :

Given :

Loan : $ 7163.84

Weekly instalment of 50$ for 3 years

Formula :

The EMI reducing-balance method is calculated using the formula shown below, in which P is the principal amount borrowed, I is the annual interest rate, r is the periodic weekly interest rate, n is the total number of weekly payments, and t is the number of weeks in a year.

(P x I) x ((1 + r)n)/ (t x ((1 + r)n)- 1)

Answer : 5.7180%