Question

Geoffrey decides not to buy the car mentioned earlier. Instead, he is now considering a food delivery service "You, bars, meats" that his friend Gillian has recently started. Gillian has agreed that for a single payment of $52,000 today to help her launch her business, she will provide all the delivery services that Geoffrey needs for his business for the next 5 years. Geoffrey is considering borrowing the full amount from his business account.

Suppose that Geoffrey makes level quarterly repayments over the coming 5 years, the first payment being exactly 3 months from today. Again, the interest rate on Geoffrey's account is 4.5% p.a. effective.

How much money does Geoffrey owe on this loan after 1 year?

Answer #1

Total Loan amount = $ 52,000

Years for which loan taken = 5 year

Amount will be paid in quarterly installment so 4 installments in a year and 20 installments in 5 years

The
mathematical formula to calculate EMI is: EMI = P × r × (1 +
r)n/((1 + r)n - 1) where P= Loan amount, r= interest rate, n=tenure
in number of months.

Rate of interest = 4.5% pa so Rate for Quaterly = 4.5%/4 = 1.125%

So EMI = $ 52000 * 1.125% * ( 1 + 1.125% )^20)/ (1 + 1.125% )^20 -1 = $ 2918

Interest Schedule for 1 st year

Installment |
Outstanding Amount at the start of Quarter |
Interest |
EMI |
Outstanding amount at the end of Quarter |

1 |
52000 |
585 |
-2918 |
49667 |

2 |
49667 |
559 |
-2918 |
47308 |

3 |
47308 |
532 |
-2918 |
44922 |

4 |
44922 |
505 |
-2918 |
42509 |

So after one year Geoffrey will owe $42509

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