Amortisation and annuities Problem set A

A loan of £12 000 charges 5.4% per year, compounded monthly, and is repaid monthly over 4 years. Find (a) the monthly payment, (b) the total repaid, (c) the total interest.

Chen can afford to repay $450 a month for 25 years. A bank charges 3.9% per year, compounded monthly. Find the largest loan Chen can take.

€150 is saved at the end of every month in an account paying 2.7% per year, compounded monthly. Find the amount after 8 years.

£200 000 is paid into a fund earning 3% per year, compounded yearly. Equal amounts are taken out at the end of each year for 20 years, emptying the fund. Find each amount.

A couple want to have $20 000 in 6 years' time for a house deposit. They pay an equal amount into an account at the end of each month. The account pays 2.4% per year, compounded monthly. (a) How much must they pay in each month? (b) How much of the $20 000 is interest?

Sofia borrows €9000 at 6% per year, compounded monthly, and repays €250 a month. How many payments does she make?

A retirement account holds $60 000 and earns 2.4% per year, compounded monthly. $800 is taken out at the end of each month. For how many months does the money last?

Tom borrows £9000 to buy a van. Option 1 charges 7.2% per year, compounded monthly, over 3 years. Option 2 charges 6.6% per year, compounded monthly, over 4 years. Both are repaid with equal payments at the end of each month. For each option find (a) the monthly payment and (b) the total repaid. (c) Which option costs less overall, and by how much?

A house loan of £180 000 charges 3.3% per year, compounded monthly, and is repaid monthly over 25 years. (a) Find the monthly payment. (b) Find the amount still owed after 10 years.