In: Finance
You have $100,000 now and will receive $130,000 in exactly one years’ time. If you spend $80,000 today and market interest rates are 10% p.a. compounded semi-annually, how much will you have in one year?
a) $130,000 b) $152,050 c) $150,000 d) $240,000 e) $240,250
Mr Simon de Money wishes to purchase a new Mercedes Benz C250 CDI. The car costs $73,200. Mr de Money has arranged a loan that only covers part of the purchase price. He intends to finance the rest of the purchase with money from his savings. The loan requires payments of $1,400 per month for 5 years. The interest rate on the loan is 12% p.a. compounded monthly. How much of his savings must Mr de Money use?
a) $13,649.87 b) $9,377.09 c) $12,639.76 d) $14,899.45 e) $10,262.95
Answer:
Part-I: Option-b) $1,52,050
At present amount in hand $1,00,000
Amount will receive exactly in one year $1,30,000
Interest Rate - 10%
Interest will be Compounded semi annually
If I spend $80,000 today then the amount in hand will be - $1,00,000-$80,000 = $20,000
Future value = present value * (1+R)n
R denotes rate of interest for the period
n denotes number of compounding periods
Here it is mentioned that the interest will be compounded semi annually
Here rate of interest for 6 months period = 10%*6months /12 months = 5%
Number of compunding periods = 12 months / 6 months = 2 periods
Future value of $ 20,000= 20,000*(1.05)2
Future value of $ 20,000= 20,000*1.1025
Future value of $ 20,000= 22,050
Therefore the amount which i have after one year = 1,30,000+22,050 = 1,52,050
Part-II:Option-e) $10.262.95
Car Cost = $73,200
He will acquire the card by taking some portion as loan and some funds from his savings
He wants to take a loan which have the following features:
Loan EMI = 1,400
Interest Rate = 12%
Period = 5 years
As the EMI is mentioned for a month then the number of months in 5 years = 5years * 12 Months = 60 months
Monthly interest rate = 12%/ 12 months = 1% per month
Loan amount = Loan EMI*present value annuity factor@1% for 6 months
Loan amount = 1400 * 44.95503
Loan amount = 62937.05
Amount he needs to take from savings to acquire the car = car cost - loan that he can be acquired
Amount he needs to take from savings to acquire the car = $73,200- 62,937.05 = $10,262.95