Question

FV/PV Annuity Problems

Problem H-4 HB 302 FV/PV Annuity Problems 1. Carly is saving to open her own business in ten vears. She currently has $10,000 and she plans to save $2,000 per year for the next five vears and $3.000 each year for the following five years. How much will she have in 10 years if she earns a 10% return on her savings? 2. What is the rate of interest on a $10,000 loan that is to be repaid in in ten equal install- ments of $1917.14? 3. You know you will need $25,000 at the end of five years. How much will you need to deposit annually, starting at the end of the first year into an investment account earning 10% to accumulate the needed amount? 4. What is the annual payment on a 30 year loan at 6% interest when $200,000 is borrowed? 5. What is the monthly payment on a 30 year loan at 6% interest when $200,000 is borrowed? 6. What amount of interest is paid with the first payment on the loan in question 57 7. What amount of interest is paid with over the life of the loan in question 5? 8. The Alpha Café rennovated its dining room for $100,000 and they owner believes over the next ten years that the benefit will be $16,273.80 per year. Determine the ROI on this rennovation

Answer 1

1)

Year	Cash flows	FVIF@10%	Future value
0	$        10,000	2.5937	$             25,937.42
1	$          2,000	2.3579	$               4,715.90
2	$          2,000	2.1436	$               4,287.18
3	$          2,000	1.9487	$               3,897.43
4	$          2,000	1.7716	$               3,543.12
5	$          2,000	1.6105	$               3,221.02
6	$          3,000	1.4641	$               4,392.30
7	$          3,000	1.3310	$               3,993.00
8	$          3,000	1.2100	$               3,630.00
9	$          3,000	1.1000	$               3,300.00
10	$          3,000	1.0000	$               3,000.00
A/c balance after 10 years			$ 63,917.37

ANSWER 2

we had to apply hit and trial method in calculating the rate of interest on loan in the below formula

(1+r) -11 FV of Annuity =P P= Periodic Payment r=rate per period n = number of periods

the rate of interest is 14% per annum

ANSWER 3

FV (r) (1+r)" - 1

P = 25000(.1)/(1.1^5)-1

= $4,094.94

RATE OF INTEREST

ANSWER 4

R P= 1-11+-NLoan

P= (.06 * 200000)/1- (1+.06)^-30=$ 14,529.78

Answer 5

R P= 1-11+-NLoan

P= by similar formula changing R and N as we get monthly oayment as $1199

ANSWER 6

interest rate number of payments com) x loan principal = interest

INTEREST ON FIRST PAYMENT WOULD BE = .06/12*200000=$1000

ANSWER 7

TOTAL AMOUNT OF INTEREST PAID DURING LIFE OF LOAN = EMI* NO. OF MONTHS - LOAN AMOUNT

= 431676 - 200000=$231676

ANSWER 8

ROI = (INFLOW/OUTFLOW) - 1

= (162738.0/100000) - 1 = 0.62738 = 62.738%

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